# 120

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```					Algebra 2

Lesson 13-2

Example 1 Draw an Angle in Standard Position
Draw an angle with the given measure in standard position.
a. 120                          b. –90
120 = 90 + 30                  The angle is negative. Draw
the terminal side of the
Draw the terminal side of the
angle 90 clockwise from
angle 30 counterclockwise
the positive x-axis.
past the positive y-axis.                     y
30 y
120
x
O          –90
O             x

Real-World Example 2 Draw an Angle in Standard Position
WAKEBOARDING Wakeboarding is a combination of surfing, skateboarding,
snowboarding, and water skiing. One maneuver involves a 450-degree rotation in the
air. Draw an angle in standard position that measures 450.
y

450 = 360 + 90                                                                               450

Draw the terminal side of the angle 90 past the                                            O     x
positive x-axis.

Example 3 Find Coterminal Angles
Find an angle with a positive measure and an angle with a negative measure that are
coterminal with each angle.
a. –250˚
A positive angle is –250˚ + 360˚ = 110˚.
A negative angle is –250˚ – 360˚ = –610˚.

π
b. -
8
             15                       16        15 
A positive angle is –           + 2π or          .       –       +          =
8              8                 8        8          8
              17                      16         17 
A negative angle is –           – 2π or –            .   –       –          =–
8                8               8        8             8
Example 4 Convert Between Degrees and Radians
Rewrite each degree measure in radians and each radian measure in degrees.
25 
a. –820˚                                        b.
3
  radians                       25  25           180 
–820 = –820                                       =     radians  
 180 

3    3             radians 

           
–82 0               41
=         radians or –                          = 1500
 18 0                 9

Real-World Example 5 Find Arc Length
Some truck tires have a radius of 21 inches. How far does a truck travel in feet after just
three fourths of a tire rotation?

Step 1   Find the central angle in radians.
3        3                 3
θ = 4  2 or 2    The angle is 4 of a complete rotation.

Step 2   Use the radius and central angle to find the arc length.
s = rθ           Write the formula for arc length.
3                                       3
= 21  2        Replace r with 21 and θ with 2 .
 98.96 in.     Use a calculator to simplify.
 8.25 ft       Divide by 12 to convert to feet.

So, the truck travels about 8 feet after three fourths of a tire rotation.

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