Exam 1 Study Guide
Math 123: College Trigonometry
February 17, 2016
1. Convert the angle measure from radians to degrees.
(a)
(b)
5π
11
15π
8
2. Convert the angle measure from degrees to radians.
(a) 45◦
(b) 345◦
3. Find the length of the arc on a circle of radius ’r’ intercepted by a central angle θ.
(a) r = 15 inches, θ = 120◦
(b) r = 3 meters, θ = 150◦
4. Find the radian measure of a central angle of a circle of radius ’r’ that intercept an arc of length ’s’.
(a) r = 80 meters, s = 150 meters
(b) r = 3 meters, s = 8 meters
5. The circular blade on a saw rotates at 5000 RPM (revolutions per minute).
(a) Find the angular speed of the blade in radians per minute
(b) The blade has a diameter of 8 inches. Find the linear speed of a blade tip.
6. A car is moving at a rate of 65 MPH (miles per hour), and the diameter of its wheels is 2 feet.
(a) Find the number of revolution per minute the wheels are rotating.
(b) Find the angular speed of the wheels in radian per minute.
7. Find the exact values for sin(t), cos(t), tan(t), csc(t), sec(t), and cot(t) at the following:
(a) t = − 5π
3
(b) t = − π4
(c) t = − 4π
3
8. Find x and r
r
32 cm
60◦
x
9. Find x and y
18 cm
y
60◦
x
10. Find y and r
y
r
60◦
10 cm
11. You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of
the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the
mountain?
12. Find the reference angle θ0 for the following angles:
(a) θ = 309◦
(b) θ = −215◦
(c) θ =
7π
6
13. Use a calculator to evaluate:
(a) sin(10◦ )
(b) cos(−110◦ )
(c) csc(−330◦ )
π
)
(d) tan(− 10
(e) cot(− 11π
)
8
(f) sec(0.29)
14. The horizontal distance d (in feet) traveled by a projectile with an initial speed v feet per second is
modeled by
v2
d=
sin(2θ)
32
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 100 feet per second
when the golf ball is hit at an angle of 50◦ . At what angle should I hit the golf ball so it travels the
farthest?
15. Find the period and amplitude for y = 3 cos(2x).
16. Find the period and amplitude for y = −3 cos( x3 ).
).
17. Find the period and amplitude for y = − 32 cos( πx
10
18. Sketch the graph for
y = 2 cos(2x)
State the period and amplitude for y.
y axis
x- axis
19. Sketch the graph for
y = 4 sin(x)
State the period and amplitude for y.
20. Sketch the graph for
x
y = sin
4
State the period and amplitude for y.
21. Sketch the graph for
y = 4 cos(x +
π
)
4
State the period and amplitude for y.
y axis
x- axis
22. Sketch the graph for
1
y = − sin
2
x
2
State the period and amplitude for y.
y axis
x- axis
23. Write an equation for the function that described by: A sine curve with a period 4π, an amplitude of
3, a left phase shift of π4 , and a vertical translation down 1 unit.
24. Write an equation for the function that described by: A cosine curve with a period of 4π, an amplitude
of 3, a right phase shift of π2 , and a vertical translation up 2 units.
25. Sketch the graph for
y = −2 tan(3x)
State the period for y.
y axis
x- axis
26. Sketch the graph for
y = tan(4x)
State the period for y.
27. Sketch the graph for
y = 3 cot(2x)
State the period for y.
y axis
x- axis
28. Sketch the graph for
y = csc
x
3
State the period for y.
y axis
x- axis
29. Sketch the graph for
y = tan(x + π)
State the period for y. Furthermore, what can you say about tan(x + π)?
y axis
x- axis
30. Sketch the graph for
y = 2 sec(3x)
State the period for y.
y axis
x- axis
−1
31. Find the exact value for cos
cos
32. Find the exact value for sin
tan
33. Find the exact value for sec
−1
−1
sin
7π
2
3
4
.
.
√ − 2
2
34. Sketch the graph for
y = 2 arctan(2x)
State the range and domain for y.
y axis
x- axis