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3.2 Angle Measures in Degrees & Radians

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3.2 Angle Measures in Degrees & Radians

Another way to measure angles is in radians.

360 = 2π rad.

180 = π rad.

–To convert from degrees to radians:

Multiply the number of degrees by

–To convert from radians to degrees:

Multiply the number of radians by

(Hint: to remember which one, think about what you want to cancel – that one goes on the bottom!)

Ex 1) Express each angle measure in radians (in terms of π)

a) 135

b) –150

Ex 2) Express each angle measure in degrees (nearest tenth)

a)

b) 5.1

Arc Length (s)

Arc length of a circle of radius r determined by central angle θ (in radians) is:

s

r

(s & r have same units)

Ex 3) Find the arc length to the nearest tenth of a cm of a circle of radius 7 cm that is intercepted by a central angle of 85

85° (convert to rad.)

Ex 4) A pendulum swings through an angle of rad. describing an arc of 0.4 m long. Determine the length of the pendulum to the nearest tenth.

0.4

sector of a circle

to find its area, we make a proportion

θ

r

Ex 5) Determine the area (to the nearest tenth of a sq. meter) of the sector of a circle of radius 1.6 m intercepted by a central angle of 45°

#302 Pg 130 #1–47 odd