Degrees to Radians
Convert 135° to radians
3𝜋/4 = 2.35
(135) x (𝜋/180) = 3𝜋/4 = 2.35
convert 𝜋 to degrees
180
(𝜋) / (𝜋/180) = 180
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 or 7.85
2(5)𝜋 = 10𝜋
90/360 = s/10𝜋
1/4 x 10𝜋 = s
s = 5𝜋/2 = 7.85
A sector with a central angle measure of 90° has a radius of 4.
What is the area of the sector?
a = 70𝜋 = 219.91
a = (90/360) x 𝜋 x (4)2
a = 70𝜋 = 219.91
A sector with a radius of 8 and central angle of 60, whats the area of shaded region
image:https://www.storyofmathematics.com/wp-content/uploads/2022/05/example-sector.png
5.80
area of sector = (60/360) x 𝜋 x 82 = 33.51
area of triangle = 1/2(8)2 x sin(60) = 27.71
33.51-27.71 = 5.80
Convert 10° to radians
𝜋/18 = 0.175
(10) x (𝜋/180) = 𝜋/18 = 0.175
convert 𝜋/3 to degrees
60
(𝜋/3) / (𝜋/180) = 60
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 or 12.57
2(10)𝜋 = 20𝜋
72/360 = s/20𝜋
1/5 x 20𝜋 = s
s = 4𝜋 = 12.57
A sector with a central angle measure of 𝜋/6 has a radius of 122.
What is the area of the sector?
3896.62
= 1/2 x (𝜋/6) x 1222
= 3896.62
A sector with a radius of 10 and central angle of 71, whats the area of shaded region
14.68
area of sector = (71/360) x 𝜋 x 102 = 61.96
area of triangle = 1/2(10)2 x sin(71) = 47.28
61.96-47.28 = 14.68
Convert 340° to radians
17𝜋/9 = 5.93
(340) x (𝜋/180) = 17𝜋/9 = 5.93
convert 13𝜋/10 to degrees
234
(7𝜋/4) / (𝜋/180) = 234
A circle with diameter 6 has an arc with a 𝜋/4 central angle.
3𝜋/4 = 2.37
l = (3)(𝜋/4)
= 3𝜋/4 = 2.37
A sector with a central angle measure of 2.45 in radians has a radius of 8.
What is the area of the sector?
l = 19.6
l = 2.45 x 8
l = 19.6
A sector with a radius of 3 and central angle of 5𝜋/6, whats the area of shaded region
9.53
area of sector = 1/2(3) x (5𝜋/6) = 11.78
area of triangle = 1/2(3)2 x sin(5𝜋/6) = 2.25
11.78 - 2.25 = 9.53
Convert 120.3° to radians
0.668𝜋 = 2.1
(120.3) x (𝜋/180) = 0.668𝜋 = 2.1
convert 5𝜋/4 to degrees
225
(5𝜋/4) / (𝜋/180) = 225
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 = 155.5°
2 x 7 = 14
x/360 = 19/14𝜋
x = 19/14𝜋 x 360
x = 155.5°
The area of a sector is 7 and radius is 2, what is the central angle, in radians(x)?
3.5
7 = 1/2 x (2)2 x (x)
7 = 2x
7/2 = x
A sector with a radius of 19.4 and central angle of 2.2 in radians, whats the area of shaded region
260.28
area of sector = 1/2(19.4)2 x (2.2) = 414
area of triangle = 1/2(19.5)2 x sin(2.2) = 153.72
414-153.72 = 260.28
Convert 43.8° to radians
0.243𝜋 = 0.764
(43.8) x (𝜋/180) = 0.243𝜋 = 0.764
convert 3𝜋/19 to degrees
28.42
(3𝜋/19) / (𝜋/180) = 28.42
A circle has a diameter of 12. It has an arc of length 11.
What is the central angle of the arc(x), in radians
x = 11/6 rad
12/2 = 6
11 = (6)x
x= 11/6
The area of a sector is 21.86 and radius is 4.8, what is the central angle, in degrees(x)?
x = 108.72
21.86 = (x/360) x 𝜋 x (4.8)2
= (x/360) x (4.8)2𝜋
21.86/(4.8)2𝜋 = x/360
x = 108.72
A sector with a radius of 3.81 and central angle of 11.75 degrees, whats the area of shaded region
0.010
area of sector = (11.75/360) x 𝜋 x 3.812 = 1.488
area of triangle = 1/2(3.81)2 x sin(11.75) = 1.478
1.488-1.478= 0.010