Name:
Math 1060
Exam 2 Review
1. Fill in the following table:
θ (radians)
θ (degrees)
sin θ
cos θ
tan θ
0
π/3
5π/6
5π/3
π
3π/2
17π/2
√
√
2/2
− 2/2
2. Fill in the following table. It may help to refer to your answers from problem 1.
θ (radians)
0
π/3
5π/6
5π/3
π
3π/2
17π/2
sec θ
csc θ
cot θ
Exam 2 Review
Math 1060
3. For each of the following functions:
• Find the amplitude, period, phase shift, and vertical shift
• Graph the function, including at least one period
(a) f (x) = 5 sin(3πx − π) + 1
(b) g(x) = −2 cos 3π
2 x+2
(c) h(t) = − sin
x
2
+ π2
4. Graph the following functions. It may help to find the period, phase shift, and vertical shift first.
(a) f (x) = tan(πx) + 1
(b) f (x) = 2 csc π2 x − π2
5. Simplify the following:
(a) sin cos−1 (x)
(b) cot sin−1 (x)
(c) sin−1 cos 3π
4
6. A lighthouse is 2 miles from the closest point on a perfectly straight shore. The light from the lighthouse is rotating; call the direction it is pointing the angle θ, where θ = 0 radians means the light is
pointing straight toward the shore. Say d is the distance from the lighthouse to the point on the shore
where the light is shining.
The paragraph above will probably be extremely confusing until you get a picture drawn.
(a) Write down a function giving the distance d in terms of the angle θ and graph it. Think carefully
about the domain of this function before you graph it!
(b) Write down a function giving the angle θ in terms of the distance d and graph it.
7. A boat is being pulled into shore by a rope. The rope is anchored to a winch on shore, which is 5 feet
above the deck of the boat. Say s is the length of the rope from the winch to the boat, and θ is the angle
of elevation from the boat to the winch.
Again, a picture will be instrumental. In this case, if you are having trouble, see problem 91 on page
350.
(a) Write θ as a function of s.
(b) Write s as a function of θ.
(c) Find θ when s = 10 feet.