perimeter of sector formula radians

A “sector” (of a circle) is bounded by an arc and two radii, so the perimeter is two times the radius (r) plus the length of the arc. Teachoo is free. It's an exciting event: ant races! Whether you want to calculate the Area (A), Arc (s), or one of the other properties of a sector including Radius (r) and the Angle formed, then provide two values of input. Perimeter of a sector. The length of the perimeter of a sector is the sum of the arc length and the two radii: = + = + = (+) where θ is in radians. Suppose the length of the arc is a cm and the angle at the centre of the circle subtended by the arc is θ radians. Solution. Sector is the portion of a disk enclosed by two radii and an arc. They are given as: Radians: A = 1 ⁄ 2 θr 2 Degrees: A = 1 ⁄ 360 θπr 2 Where A is the area, θ is the sector angle, and r is the radius. Perimeter of an ellipse formula (ellipse circumference formula) Although the formula for the area of an ellipse is really simple and easy to remember, the perimeter of an ellipse formula is the most troublesome of all the equations listed here. Sector area formula. This means that in any circle, there are 2 PI radians. 625 = 18 x 18 x θ/2. 1 decade ago "measure of the angle x radius"..since you are measuring a distance the angle must be in radians. A1837-16∘, 0.7 rad B3714-32'∘, 0.7 pleased C1837-16'∘, 0.3 rad D3714-32'∘, 0.3 rad No.24: the length of the arc of the sector is 33 cm, and the perimeter of 67 cm. Then, simplify the formula and the formula for area of sector when angle Ө is in radians will then be derived as Area = (1/2) X r²Ө. The perimeter will be the distance around this sector, which is a radius plus a radius plus an arc length. If s is arc length (i.e. We know that the perimeter would be the distance all the way around. Ask Question + 100. The area of the sector … Perimeter of sector will be the distance around it, = 2 ((π + 2 × 4)/4)= 2 ((π + 8)/4) = (π + 8)/4 cm, Subscribe to our Youtube Channel - https://you.tube/teachoo. Teachoo provides the best content available! Answer Save. We’re looking for the perimeter of this sector. 1 0. Perimeter of sector = r + 2r = r( + 2) Where is in radians If angle is in degrees, = Angle × π/(180°) Let us take some examples: Find perimeter of sector whose radius is 2 cm and angle is of 90° First, We need to convert angle in radians = Angle in degree × π/(180°) = 90° × π/(180° ) = π/4 For the full circle, the angle is 2π radians and the perimeter is the circumference which is 2πr, i.e. C2 Trigonometry: Arc Length & Sector Area PhysicsAndMathsTutor.com Edexcel Internal Review 3 (a) Show that the surface area of the box, S cm . Circular sector. Area of a sector = (θr 2)/2. Calculates area, arc length, perimeter, and center of mass of circular sector. Perimeter of sector and area of sector: Trigonometry: Feb 6, 2016: Finding area of a sector and the measure of part of circumference of a circle: Geometry: Aug 23, 2015: Finding areas of sectors using radians: Trigonometry: Feb 15, 2013 You've set up a tiny track around the outside edge of a slice of pizza. A sector of angle 5π/12 radians is cut from a circle of radius 6 cm. Perimeter is the distance around a two-dimensional shape. Digits after the decimal point: 2. First, we want to just sketch our circle and then label each part. Get your answers by asking now. Arc Length = θr. perimeter of sector), r is radius and θ is angle of sector then: s = r*θ where θ is in radians (s = r*θ*pi/180 if θ is in degrees: this is the equivalent of your expression: s = r*θ*2pi/360) In a semi-circle, there is no major or minor sector. Calculation precision. Sector area formula. He has been teaching from the past 9 years. On signing up you are confirming that you have read and agree to So in the below diagram, s = r∅ . Learn how tosolve problems with arc lengths. Example 10: Find the perimeter of a sector with central angle 60 and radius 3 in. Find the perimeter of the sector to the nearest centimeter. Comparing the area of sector and area of circle, we get the formula for the area of sector when the central angle is given in radians. Favorite Answer. We are given the radius of the sector so we need to double this to find the diameter. 2 Answers. Radius. Substitute 10 for r. l + 2 (10) = 45. l + 20 = 45. l = 45 - 10. l = 35 cm. What is the formula for the perimeter of a sector in terms of radians? The sector has radius r cm and angle 1 radian. Angle in degrees. Area enclosed by an arc of a circle or Area of a sector = (θ/360 o ) x πR 2. Angles will be in Radians or Degrees. The formula for a sector's area in radians is: A = (sector angle / (2*pi)) * (pi * r 2) Area and Known Portions of a Circle. One of the sectors measures 40 degrees. Find the length of arc, if the perimeter of sector is 45 cm and radius is 10 cm. Examples. So if a sector of any circle of radius r measures θ, area of the sector can be given by: Area of sector = \(\frac{\theta }{360} \times \pi r^{2}\) Derivation: If s is arc length (i.e. Example: a) What is the length of the arc intercepted by an angle of 15° on a circle with radius 20 meters? We’re also interested in the perimeter of this sector. Videos, worksheets, 5-a-day and much more Sector area is found $\displaystyle A=\dfrac{1}{2}\theta r^2$, where $\theta$ is in radian. The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). Solution : Perimeter of sector = 45 cm. I know the formula for arc length is rθ. Perimeter and Sector Defined. In geometry, a sector of a circle is made by drawing two lines from the centre of the circle to the circumference. Perimeter of sector is = l + 2r Substitute l = 44 and r = 21. Now we just need to use our common sense. This sector has a minor arc, because the angle is less than 180⁰. ... Lv 7. Answer Save. Radians, like degrees, are a way of measuring angles. Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. Let the angle made between the 2 radii that have resulted in the formation of that sector, be equivalent to “x”. one radius per one radian, which is pretty much the how and why of "radian's" existence. These are sectors that are an eighth circle, quarter circle, and semicircle. Angle. Area of a sector formula. You know the length of the radii so what remains is to find the length of the arc. Anonymous. Recall that the angle of a full circle in radians is 2π. The arc length formula is used to find the length of an arc of a circle; $ \ell =r \theta$, where $\theta$ is in radian. Formula For Area Of Sector (In Radians) Next, we will look at the formula for the area of a sector where the central angle is measured in radians. For a sector the area is represented by some other angle. One radian is equal to the angle formed when the arc opposite the angle is equal to the radius of the circle. = 44 + 2 (21) So one radian = 180/ PI degrees and one degree = PI /180 radians. If the measure of the arc (or central angle) is given in radians, then the formula for the arc length of a circle is. Just replace 360˚ in the formula by 2π radians (note that this is exactly converting degrees to radians). A sector of a circle has a perimeter made up of two radii and an arc of the circle connecting the endpoints of the two radii. The arc is the outer edge of the sector. Circular sector. = 9×80°π/180 = 12.57 cm. Let this region be a sector forming an angle of 360° at the centre O. These are the conversion formulas for radians to degrees and for degrees to radians, respectively. The following video shows how this formula is derived from the usual formula of Area of sector = (Ө/360˚) X πr². We can find the perimeter of a sector using what we know about finding the length of an arc. Therefore 360º = 2 PI radians. the perimeter of a sector is rθ + 2r*sin(θ/2) 0 0. Example 1 : Find the perimeter of the sector PQR shown below. So in the below diagram, the shaded area is equal to ½ r² ∅ . The formula for finding the area of a circle is pi*r*r where r is the radius. 0 5. Area of sector formula and examples- The area of a sector is the region enclosed by the two radius of a circle and the arc. 1. Arc length . One of the sectors measures 40 degrees. The length of an arc of a circle is equal to ∅, where ∅ is the angle, in radians, subtended by the arc at the centre of the circle (see below diagram if you don’t understand). Formula For Area Of Sector (In Radians) Next, we will look at the formula for the area of a sector where the central angle is measured in radians. We have a radius of seven centimeters. The length of the perimeter of a sector is the sum of the arc length and the two radii: {\displaystyle P=L+2r=\theta r+2r=r (\theta +2)} where θ is in radians. r S r. 2 = + 1800 (5) (b) Use calculus to find the value of r for which S is stationary. We know that a full circle is 360 degrees in measurement. Source(s): ... where θ is in radians. Formula to find length of the arc is l = θ/36 0 ° ⋅ 2 ∏ r. Formula to find area of sector is A = θ/360 ° ⋅ ∏r 2 square units. He provides courses for Maths and Science at Teachoo. Yes, it is rθ+2r. Perimeter. Mein Hoon Na. Problem 7 : Find the radius of sector whose perimeter of the sector is 30 cm and length of the arc is 16 cm. Copyright © 2004 - 2020 Revision World Networks Ltd. Relevance. Therefore 360º = 2 PI radians. Imagine yourself standing at O and walking to A along the radius, then from A to B along the arc, … where r is the radius of the circle. 1 decade ago. The circumference of the circle is 2 (pi)r and it covers 360 degrees. This sector has a minor arc, because the angle is less than 180⁰. You will learn how to find the arc length of a sector, the angle of a sector or the radius of a circle. It's also very important to remember to have a calculator set to "radians" and NOT "degrees", when working out the sin value. For a circle, that entire area is represented by a rotation of 360 degrees. 1 decade ago. To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). Answer Save. the perimeter of a sector is the distance around it. The “perimeter” of any closed shape is simply the sum of the lengths of all of its boundaries. The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2; But where does it come from? Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). We have seen in this section how we are supposed to calculate area and perimeter of circle and arc. A sector of angle 5π/12 radians is cut from a circle of radius 6 cm. The sector is formed of two radii and the arcual length, so the perimeter of the sector =2r + 2 (pi)r* (theta/360) It's also very important to remember to have a calculator set to "radians" and NOT "degrees", when working out the sin value. l + 2r = 45. The formula for the length of an arc is:: 570 = where L represents the arc length, r represents the radius of the circle and θ represents the angle in radians … MALATHI VEDAGIRI. The radius of a circle is seven centimeters and the central angle of a sector is 40 degrees. one radius per one radian, which is pretty much the how and why of "radian's" existence. A sector is formed between two radii and an arc. Area of sector formula and examples- The area of a sector is the region enclosed by the two radius of a circle and the arc. Arc Length = 14 × 2.4 = 33.6 10 POPPER FOR SECTION 4.2: Question#2: Find the area of a sector that has radius 12 inches and central angle 6 . Yes, it is rθ+2r. With the relevant angle given in radians here, the sums changes slightly, but still give a good measure of segment perimeter. There are two sector area formulas; one for a sector measured in radians, and another for a sector measured in degrees. Sometimes, the portion of a circle is known. ... Sector Perimeter = r(θ+2) r = radius θ = angle in radians : Ellipse Perimeter = very hard! For the full circle, the angle is 2π radians and the perimeter is the circumference which is 2πr, i.e. Example 1 Find the arc length and area of a sector of a circle of radius $6$ cm and the centre angle $\dfrac{2 \pi}{5}$. Worksheet to calculate arc length and area of sector (radians). Recall that the angle of a full circle in radians is 2π. Arc Length Formula - Example 1 Discuss the formula for arc length and use it in a couple of examples. The perimeter of the sector includes the length of the radius $\times 2$, as well as the arc length.So the perimeter is the length "around" the entire sector, the length "around" a slice of pizza, which includes it's edges and its curved arc.. Example 1 . Example: the perimeter of this rectangle is 7+3+7+3 = 20. Worked solution to a question involving arc length and perimeter of a sector So one radian = 180/ PI degrees and one degree = PI /180 radians. We’re looking for the perimeter of this sector. The Corbettmaths Practice Questions on the Area of a Sector. 0 0. Anonymous. To find the perimeter, we need to add these values together. Learn Science with Notes and NCERT Solutions, Area of combination of figures - two circles, circle and square, Finding Area of rectangle with path outside/inside, Finding Area of rectangle with cross roads. The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2; But where does it come from? Terms of Service. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! Best Answer. 2, is given by . Comparing the area of sector and area of circle, we get the formula for the area of sector when the central angle is given in radians. Anonymous. So the circumference of a circle is 2 PI larger than its radius. See the video below for more information on how to convert radians and degrees. The formula for a sector's area in radians is: A = (sector angle / (2 ... An isosceles triangle is inscribed in a circle that has a diameter of 12 in. ): The area of a circle is calculated as A = πr². My question says a sector of a circle has a radius of 9 cm and the angle is 80 degrees find the perimeter of the sector? Help Fast!!! If the radius of the sector is 18 mm, find the central angle of the sector in radians. The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. This means that in any circle, there are 2 PI radians. Then, the area of a sector of circle formula is calculated using the unitary method. To convert a certain number of radians into degrees, multiply the number of radians by 180/ PI . metres), and area will be in unit squares (e.g. where θ is the measure of the arc (or central angle) in radians and r is the radius of the circle. Therefore 180º = PI radians. So in the above diagram, the angle ø is equal to one radian since the arc AB is the same length as the radius of the circle. We usually use the variable to represent the arc length. The volume of the box is 300 cm3. We are given the radius of the sector so we need to double this to find the diameter. Lv 7. As we know mathematics is not a spectator sport so we also got through its application in some practical examples of area and perimeter related to circle and arc. 1 decade ago. Find the central angle gives the answer for the nearest second. Solved Example The below solved example problem may be useful to understand how the values are being used in the mathematical formulas to find the sector area of … Now, the circumference of the circle is 2 PI r, where r is the radius of the circle. person_outlineAntonschedule 2011-05-06 20:21:55. In this calculator you can calculate the perimeter of sector of circle based on the radius and the central angle. Convert 330° to radians. perimeter of sector), r is radius and θ is angle of sector then: s = r*θ where θ is in radians (s = r*θ*pi/180 if θ is in degrees: this is the equivalent of your expression: s = r*θ*2pi/360) Section 4.2 – Radians, Arc Length, and the Area of a Sector 4 Sector Area Formula In a circle of radius r, the area A of a sector with central angle of radian measure T is given by . The perimeter is the distance all around the outside of a shape. What is the formula for the perimeter of a sector? 1 0. Worksheet to calculate arc length and area of sector (radians). I know the formula for arc length is rθ. The perimeter of a sector is composed of three pieces, an arc of the circle and two radii. A sector of a circle is the shape formed by slicing up a circular cake. The following mathematical formula is used in this circular sector calculator to find the area for the given input values of radius r & the angle θ in degrees. or A = rl / 2 square units. Login to view more pages. What is the formula for the perimeter of a sector in terms of radians? in the Radians giving an answer to one decimal place. There is a lengthy reason, but the result is a slight modification of the Sector formula: Perimeter. so does that mean the perimeter of a sector is rθ+2r??? Yes, though it can be expressed more simply. First, we want to just sketch our circle and then label each part. Find the perimeter of the sector to the nearest centimeter. Relevance. Compare the areas of three sectors -- each with P = 100 -- central angles of 45 degrees, 90 degrees, and 180 degrees. Exercise worksheet on 'Find the area of a sector of a circle when the angle is given in radians.' What is the formula to find the perimeter of a sector of a circle? so does that mean the perimeter of a sector is rθ+2r??? The formulas to find the area of a sector in Degrees (D°) or Radians (R°) are shown below: Area (Degrees) = πr 2 x θ/360. A) 2 B) 4 C) 72 D) 144 E) 12 F) None of these . Sector area is found $\displaystyle A=\dfrac{1}{2}\theta r^2$, where $\theta$ is in radian. You can work out the Area of a Sector by comparing its angle to the angle of a full circle.Note: we are using radians for the angles.This is the reasoning: Area of Sector = θ 2 × r2 (when θ is in radians)Area of Sector = θ × π 360 × r2 (when θ is in degrees) Yes, though it can be expressed more simply. Area (Radians) = ½r 2 θ. r, D° r, R° r, s r, A D°, s. Radius (r) Angle (D°) Angle (R°) Arc (s) Area (A) *Radius and Arc in units (e.g. Solution : You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! 3 Answers. 1) In the video lesson, we learned that the perimeter of a sector of a circle, like a slice of pizza, is the sum of two edges that are both the radius and the edge that is the arc length. Arc length. Still have questions? ): The area of a circle is calculated as A = πr². Anonymous. To find that arc length, we start with our central angle in radians and we multiply it by the radius. Understanding the problem. The formula for the area of a sector is (angle / 360) x π x radius 2.The figure below illustrates the measurement: As you can easily see, it is quite similar to that of a circle, but modified to account for the fact that a sector is just a part of a circle. Section 4.2 – Radians, Arc Length, and the Area of a Sector 4 Sector Area Formula In a circle of radius r, the area A of a sector with central angle of radian measure T is given by . Anonymous . 1 decade ago. Calculate. 1 decade ago. With the relevant angle given in radians here, the sums changes slightly, but still give a good measure of segment perimeter. The formula for the area of a sector is (angle / 360) x π x radius 2.The figure below illustrates the measurement: As you can easily see, it is quite similar to that of a circle, but modified to account for the fact that a sector is just a part of a circle. Relevance. This formula helps you find the area, A, of the sector if you know the central angle in degrees, n °, and the radius, r, of the circle: A = ( n ° 360 ° ) × π × r 2 For your pumpkin pie, plug in 31 ° and 9 inches: where 'l' is the length of the minor arc AB. Practice Questions. This page includes a lesson covering 'finding the area of a sector of a circle when the angle is given in radians' as well as a 15-question worksheet, which is printable, editable, and sendable. Perimeter of Sector of Circle Calculator. Select the input value you want, then enter their values. metre 2). Arc Length Formula - … b) What is the length of the arc intercepted by an angle of 210° on a circle with radius 2.9 ft? Formula to find perimeter of the sector is = l + 2r. Area of a circle is given as π times the square of its radius length. Find the arc length and area of a sector of a circle of radius $6$ cm and the centre angle $\dfrac{2 \pi}{5}$. 625 = 162 θ. Divide both sides by 162. θ = 3.86 radians. Therefore 180º = PI radians. Favorite Answer. Circle Sector Perimeter = r * (α + 2) where α is in radians. 1. So the length of the arc of the sector = 2 (pi)r* (theta/360). 1 decade ago. Try It Yourself Geometry Index. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² When the angle at the center is 1°, area of the sector = … We have a radius of seven centimeters. Area of Sector = θ 2 × r 2 (when θ is in radians) Area of Sector = θ × π 360 × r 2 (when θ is in degrees) Area of Segment. 3 Answers. To convert a certain number of radians into degrees, multiply the number of … Arc Length = 14 × 2.4 = 33.6 Area of a sector formula. \Theta r^2 $, where r is the distance all the way around PI r, where $ \theta is... 14 × 2.4 = 33.6 these are sectors that are an eighth circle, the angle is 2π calculate area. 30 cm and angle 1 radian three pieces, an arc of the sector in is. Circle area formula ( and we bet you do 2π radians and we you. ( e.g the central angle in radians here, the angle of the sector is 18 mm, the! To radians ) PI ) r * ( theta/360 ) per one radian, which is a graduate Indian! Disk enclosed by two radii and an arc has been teaching from the usual formula of area a. Length and area of a full circle in radians here, the area of a circle is the.. First, we want to just sketch our circle and then label each.. We are supposed to calculate area and perimeter of a circle when the arc length by a rotation of degrees! Of all of its boundaries 1 } { 2 } \theta r^2 $, where r is shape. And then label each part certain number of radians 20 meters a disk enclosed by an arc of circle... And one degree = PI /180 radians. sector forming an angle of 15° on a circle when angle... Formula of area of a circle of radius 6 cm If the radius of examples one a. Want, then enter their values what remains is to find the perimeter of a sector is 18,... To radians, and another for a sector of circle formula is derived the... Region be a sector in radians. and angle 1 radian mm, find perimeter! Is rθ+2r??????????????????... We need to remember is circle area formula ( and we bet you do is 30 cm length! That a full circle, quarter circle, the portion of a full circle in radians here the... Formula is calculated using the unitary method nearest centimeter, are a way of measuring angles way of measuring.! Why of `` radian 's '' existence in any circle, quarter circle, quarter circle, and...., worksheets, 5-a-day and much more a sector, which is a graduate from Indian Institute of,! Davneet Singh is a lengthy reason, but still give a good measure of segment.! Radius length example 1 Discuss the formula for arc length = 14 × 2.4 = 33.6 these are conversion... Double this to find the central angle in radians is cut from a circle is 2 PI than! Of sector ( radians ) the nearest second this section how we are supposed to calculate area... The equivalent circle using the unitary method radii so what remains is to find the of. Radians and r is the length of the radii so what remains is to find perimeter of sector. Relevant angle given in radians here, the angle is less than 180⁰ formula: of! For radians to degrees and for degrees to radians, respectively add these values together 360!, that entire area is found $ \displaystyle A=\dfrac { 1 } { 2 \theta. Sector PQR shown below of `` radian 's '' existence radius and the perimeter of whose... This is exactly converting degrees to radians, respectively around this sector a! The arc is the area of a sector of perimeter of sector formula radians and then label each part r! And degrees calculate area and perimeter of this sector has radius r cm and length of circle! It by using proportions, all you need to remember is circle area formula ( and we bet you!! Formula: area of a circle or area of sector of angle 5π/12 radians is.... The distance around this sector triangular piece ( shown in light blue here ) 2πr, i.e you set! This is exactly converting degrees to radians ) by 2π radians and we you... ; one for a sector of angle 5π/12 radians is cut from a is. A minor arc AB equal to ½ r² ∅: a ) what is the of. ’ re looking for the perimeter of the arc '' existence Institute of Technology,.. Metres ), and center of mass of circular sector usually use variable... 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Know about finding the length of the sector so we need to double this to find perimeter of sector... The shape formed by slicing up a circular cake 1 radian the way around our! Radius 6 cm radians and the perimeter of a slice of pizza α + )... The radii so what remains is to find the diameter x πr² shown! Minus the triangular piece ( shown in light blue here ) shown light. ) 72 D ) 144 E ) 12 F ) None of these for the perimeter of of! Eighth circle, quarter circle, the sums changes slightly, but the result is a graduate from Institute! More simply from the centre O radian is equal to ½ r² ∅ Practice Questions on the radius the. Is pretty much the how and why of `` radian 's '' existence is 360 degrees common sense θ/2 0. The shape formed by slicing up a circular cake be in unit squares ( e.g is 2 PI radians '. Is circle area formula ( and we bet you do angle 60 and radius 3 in by proportions... Calculate area and perimeter of a sector is rθ+2r???????! 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Θ/2 ) 0 0 on how to find the diameter and why of `` radian ''... Composed of three pieces, an arc + 2r arc, because the x... ), and another for a sector is the length of an arc of a sector is rθ+2r?. Formula - example 1: find the perimeter of a segment is the for! The unitary method derived from the centre of the equivalent circle using the formula arc. About finding the length of the sector is rθ+2r????????. Piece ( shown in light blue here ) and then label each.... The radius of the arc is 16 cm $, where $ \theta $ is radian... Is 18 mm, find the perimeter, we need to use our common sense we can find by... Sums changes slightly, but still give a good measure of segment.. Is equal to ½ r² ∅ less than 180⁰: area of a sector using we. Slightly, but the result is a lengthy reason, but the result is a slight modification the. Example 1 Discuss the formula to find the perimeter of sector ( radians ) common! The formula for arc length, perimeter, we need to use our common.... Our common sense equal to the radius of the sector is 30 cm angle! Of 15° on a circle with radius 20 meters is less than 180⁰ from the past years! Radian = 180/ PI E ) 12 F ) None of these drawing two lines from the past years... Terms of Service ½ r² ∅ the sector PQR shown below radians and r is formula! = very hard ago `` measure of segment perimeter up you are measuring a the... This section how we are supposed to calculate arc length formula - … If the radius 6 cm radii an... Calculate arc length means that in any circle, the portion of a sector is composed of three pieces an! More information on how to convert a certain number of radians exactly degrees!