Degrees to Radians
How many radians is 45°?
45° is 𝜋/4 radians
45° x 𝜋 radians/180°
= 45𝜋/180 radians
= 𝜋/4 radians
Convert 90° to radians
𝜋/2
𝜋/180 x 90 = 90𝜋/180 = 9𝜋/18 = 𝜋/2
A circle has a radius of 5. An arc in this circle has a central angle of 90°
What is the length of the arc?
s = 5𝜋/2
2(5)𝜋 = 10𝜋 ~ 90/360 = s/10𝜋 ~ 1/4 x 10𝜋 = s
s = 5𝜋/2
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How many radians is 30°?
30° is 𝜋/6 radians.
= 𝜋/6 radians
Convert 120° to radians
2𝜋/3
𝜋/180 x 120 = 120𝜋/180 = 12𝜋/18 = 2𝜋/3
A circle has a radius of 10. An arc in this circle has a central angle of 72°
What is the length of the arc?
4𝜋
2(10)𝜋 = 20𝜋 ~ 72/360 = s/20𝜋 ~ 1/5 x 20𝜋 = s
s = 4𝜋
A sector with a central angle measure of 175° has a radius of 12.
What is the area of the sector?
a = 70𝜋
175/360 = a/144𝜋 ~ 175/360 x 144𝜋 = a
a = 70𝜋
How many radians is 150°?
150° is 𝜋/6 radians.
150° x 𝜋 radians/180° = 150𝜋/180 radians
= 5𝜋/6 radians
Convert 230° to radians
23𝜋/18
𝜋/180 x 230 = 230𝜋/180 = 23𝜋/18
A circle with circumference 6 has an arc with a 340° central angle.
What is the length of the arc?
s = 17/3
340/360 = s/6 ~ 17/18 = s/6 ~ 17/18 x 6 = s
s = 17/3
A sector with a central angle measure of 𝜋/6 (in radians) has a radius of 122.
What is the area of the sector?
𝜋(12)^2= 144𝜋 (area of whole circle)
(𝜋/6)/2𝜋 = a/144𝜋 ~ (𝜋/6)/2𝜋 x 144𝜋 = a
a = 12𝜋
How many radians is 3°?
3° is 𝜋/60 radians.
3° x 𝜋 radians/180° = 3𝜋/180 radians
= 𝜋/60 radians
Convert 135° to radians
3𝜋/4
𝜋/180 x 135 = 135𝜋/180 = 3𝜋/4
A circle has a radius of 7. It has an arc of length 19.
What is the central angle of the arc, in degrees (x)
x = 265°
2 x 7 = 14
x/360 = 14/19 ~ x = 14/19 x 360
x = 265°
A sector with a radius of 8 has an area of 56𝜋
What is the central angle measure of the sector in radians?
x = 7𝜋/4
𝜋(8)^2 = 64𝜋
x/2𝜋 = 56𝜋/64𝜋 ~ x = 56𝜋/64𝜋 x 2𝜋 ~ x = 7/8 x 2𝜋
x = 7𝜋/4
How many radians is 278°?
278° is 139𝜋/90 radians.
278° x 𝜋 radians/180° = 278𝜋/180 radians
= 139𝜋/90 radians
Convert 348° to radians
29𝜋/15
𝜋/180 x 348 = 348𝜋/180 = 29𝜋/15
A circle has a circumference of 12. It has an arc of length 11.
What is the central angle of the arc, in radians
x = 11𝜋/6
x/360 = 11/12 ~ x = 11/12 x 360
x = 330 ~ 330𝜋/180 ~ 11𝜋/6 = x
x = 11𝜋/6
A sector with a circumference 36 has an area of 234𝜋
What is the central angle measure of the sector in degrees?
x = 260
36/2 = 18
𝜋(18)^2= 324𝜋
x/360 = 234𝜋/324𝜋 ~ x = 234𝜋/324𝜋 x 360
x = 260