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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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