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Chapter 4 Trigonometric Functions

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<strong>Trigonometric</strong> <strong>Functions</strong><br />

7. a. 855°− 360°⋅ 2 = 855°− 720°= 135°<br />

b.<br />

c.<br />

17π<br />

17π<br />

−2π<br />

⋅ 2= − 4π<br />

3 3<br />

17π 12π 5π<br />

= − =<br />

3 3 3<br />

25π<br />

25π<br />

− + 2π<br />

⋅ 3=− + 6π<br />

6 6<br />

25π 36π 11π<br />

=− + =<br />

6 6 6<br />

8. The formula s = rθ can only be used when θ is<br />

expressed in radians. Thus, we begin by converting<br />

π radians<br />

45° to radians. Multiply by .<br />

180°<br />

π radians 45<br />

45°= 45 °⋅ = π radians<br />

180°<br />

180<br />

π<br />

= radians<br />

4<br />

Now we can use the formula s = rθ to find the<br />

length of the arc. The circle’s radius is 6 inches : r =<br />

6 inches. The measure of the central angle in radians<br />

π π<br />

is : θ = . The length of the arc intercepted by this<br />

4 4<br />

central angle is<br />

⎛π<br />

⎞ 6π<br />

s = rθ<br />

= (6 inches) ⎜ ⎟= inches ≈ 4.71 inches.<br />

⎝ 4⎠<br />

4<br />

9. We are given ω , the angular speed.<br />

ω = 45 revolutions per minute<br />

We use the formula ν = rω<br />

to find v , the linear<br />

speed. Before applying the formula, we must express<br />

ω in radians per minute.<br />

45 revolutions 2 π radians<br />

ω = ⋅<br />

1 minute 1 revolution<br />

90 π radians<br />

=<br />

1 minute<br />

The angular speed of the propeller is 90π radians per<br />

minute. The linear speed is<br />

90π<br />

135 π inches<br />

ν = rω<br />

= 1.5 inches ⋅ = 1 minute minute<br />

The linear speed is 135π inches per minute, which is<br />

approximately 424 inches per minute.<br />

Exercise Set 4.1<br />

1. obtuse<br />

2. obtuse<br />

3. acute<br />

4. acute<br />

5. straight<br />

6. right<br />

7.<br />

8.<br />

9.<br />

10.<br />

11.<br />

12.<br />

13.<br />

14.<br />

θ = s 40 inches<br />

4 radians<br />

r<br />

= 10 inches<br />

=<br />

θ = s 30 feet<br />

6 radians<br />

r<br />

= 5 feet<br />

=<br />

s 8 yards 4<br />

θ = = = radians<br />

r 6 yards 3<br />

θ = s 18 yards<br />

2.25 radians<br />

r<br />

= 8 yards<br />

=<br />

θ = s 400 centimeters<br />

4 radians<br />

r<br />

= 100 centimeters<br />

=<br />

θ = s 600 centimeters<br />

6 radians<br />

r<br />

= 100 centimeters<br />

=<br />

π radians<br />

45°= 45°⋅<br />

180°<br />

45π<br />

= radians<br />

180<br />

π<br />

= radians<br />

4<br />

π radians<br />

18°= 18°⋅<br />

180°<br />

18π<br />

= radians<br />

180<br />

π<br />

= radians<br />

10<br />

15.<br />

π radians<br />

135°= 135°⋅<br />

180°<br />

135π<br />

= radians<br />

180<br />

3π<br />

= radians<br />

4<br />

490<br />

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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