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Chapter 6 – Review
Be able to do pretty much everything without a calculator
Section 6.1
DMS to Decimal degrees and back
linear and angular speed
arclength and sector area
1. Convert to Decimal: 60 45’12”
2. Convert to DMS (degrees minutes seconds): 42.5125
3. To make a clay vase, an artist uses a potter’s wheel that has a diameter of 13 in. and
spins at 120 rpm. Find the approximate distance traveled in 1 min by a point on the outer
edge of the wheel.
4. Jay wants to paint the six colors of the rainbow around a cylindrical column. She
paints 1/6 of the way around red then the next sixth orange, etc. until she uses all six
colors. The radius of the column is five feet. What is the arc length of each color?
5. Arnie wants to know how fast he rides his bike. The wheels are 26 inches in diameter
and he counts the wheels rotating at thirty revolutions per 10 seconds. What is his speed
in miles per hour?
Section 6.2
Find the six trigonometric functions for a given angle on the unit circle or not or if given
a point on the circle.
6. Find the exact value of each

a. sin 30
b. cos
c. tan 135
2
7. (-3, -4) is a point on the terminal side of an angle, θ in standard position. Find the
exact values of the six trigonometric functions of θ.
Section 6.3
Find the domain and range of a trig function
Use periodic properties to find the value of a trig function outside of the 0 to 2π circle
Use reciprocal and quotient identities to find exact values.
Know the even-odd properties
8. Find the domain and range of y = 4sin3θ
5
9. Find the exact value of each: a. sin 765 b. cos 
c. tan -855
6
1
10. Find the exact value:
- sin2(-22)
2
sec (22)
Section 6.4
Be able to graph the sine and cosine functions and find the 5 key points
Find the Amplitude and period of a sine or cosine function.
11. Find the Amplitude and period and graph y = -3sin (4θ) – 4 by finding the 5 key
points.
12. Find the Amplitude and period and graph y = 5sin (1.5θ) by finding the 5 key points.
Section 6.5
Be able to graph the remaining four functions. (tangent, cotangent, secant and cosecant)
13. Graph y = 7tan(3θ – π)
14. Graph y = ½ csc(θ) + 2
Section 6.6
Solve word problems involving Sinusoidal functions
Graph any sinusoidal function with a phase shift
Be able to build a sinusoidal function from data.


cos(  )
3 4
15. Find the amplitude, period and phase shift and graph y 
2
16. Model the data with a Sinusoidal function
Month, m
Jan, 1
Feb, 2
Mar, 3
Apr, 4
May, 5
June, 6
Jul, 7
Aug, 8
Sep, 9
Oct, 10
Nov, 11
Dec,12
Average
Monthly
Temperature,
T, in Phoenix,
Arizona
51
55
63
67
77
86
90
90
84
71
59
52
answers: 1. 60.75 2. 4230’45” 3. 4901 in. 4. 5.24 feet 5. 13.9 mph 6a. ½ b. 0 c. -1 7. sin θ
=
4
3
4
cos θ =
tan θ = csc θ =
5
5
3
2
 3
5
5
3

sec θ =
cot θ = 8. D: all Reals R: -4 ≤ y ≤ 4 9a.
b.
c. 1 10. 1 11. Amp = 3 period =
12. Amp = 5, per =
4
3
4
2
2
2
4
13.
3
14.
2 

x
  70.5
3 
6
16. 19.5sin 
15. Amp = ½ per = 6π, phase shift =
3
4