3 2 angle measures in degrees radians
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3.2 Angle Measures in Degrees & Radians PowerPoint PPT Presentation


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3.2 Angle Measures in Degrees & Radians. Another way to measure angles is in radians. 360  = 2 π rad.  18 0 = 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

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3.2 Angle Measures in Degrees & Radians

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3 2 angle measures in degrees radians

3.2 Angle Measures in Degrees & Radians


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!)


3 2 angle measures in degrees radians

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


3 2 angle measures in degrees radians

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.)


3 2 angle measures in degrees radians

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


3 2 angle measures in degrees radians

sector of a circle

to find its area, we make a proportion

θ

r


3 2 angle measures in degrees radians

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°


Homework

Homework

#302 Pg 130 #1–47 odd


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