1. Graph two complete cycles of the following. Label all maximum and minimum values.

Minimum points: maximum points:

List the following information:

Amplitude: __3/2______

Period: ____π/3______

Phase Shift: __- π/2______

Vertical Shift: _down 1______

Reflection: __yes_ (yes or no)

Domain: ______

Range: __[-5/2, ½]______

2. The point (-5,11) is on the terminal side of angle θ in standard position. Find the exact value of cos θ.

3. Write and equation for a sinusoidal graph with the following properties:

A= -3 period = phase shift =

4. Find the reference angle for the following:

a) b)

5. Use a coterminal angle to find the exact value of each expression.

a) = b) =1

6. Find the exact value of the following expressions:

a) = b) =

c) = d) =

e) =

7. Verify the following identity. Work with one side only. Show all steps!

Verify:

8. Solve the following equations both in general and on the interval [0,2π).

a)

Using double angle formula and simplifying the equation we get:, , , or , where k is any integer. And then on , are the solutions

b)

After factoring, we get that or . Since 4 is outside the range of cosine, we only consider . So we have: or , k is any integer. And then on , or are the solutions

c)

if you solved for cosecant: or

if you solved for cotangent: , all where k is an integer

Then, on , or are the solutions

d)

So or . Therefore, or

And then on , the solution set is {}

9. Find the length of the arc subtended by a central angle of 37° on a circle of diameter 4 feet. ANSWER: 1.29 feet

10. If and , find the exact value of the following:

a) = b) = c) =-4/5 d) =-3/5

e) = f) = g) =

11. A hot air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, AL. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport?

1.30°

12. Solve the following triangles (if one exists). If two triangles exist, solve both.

a) b)

no triangle exists

c)

13. Madison wants to swim across a lake from the fishing lodge (A) to the boat ramp (B) but she wants to know the distance first. Highway 20 goes right past the boat ramp and County Road 3 goes to the lodge. The two roads intersect at point (C), 4.2 miles from the ramp and 3.5 miles from the lodge. The angle of intersection of the two roads is 32°. How far will she need to swim?

2.23 miles

14. Two ships leave port at 4 p.m.One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour.The other is traveling 13 miles per hour at a bearing of S 47 E.How far apart are they when dinner is served at 6 p.m.?

36.18 miles

15. A building is of unknown height. At a distance of 100 feet away from the building, an observer notices that the angle of elevation to the top of the building is 41º and that the angle of elevation to a poster on the side of the building is 21º. How far is the poster from the roof of the building?

48.54 feet

16. Determine the EXACT values of A, ω, and B so that the graph below is given by the function of the form

a) =

b) =

17. Complete the following table.

Domain / Range / Period/ / [-1,1] / 2π

/ / [-1,1] / 2π

/ except odd multiples of kπ/2

Or could be written as: except at π/2 + πk / / π

/ except at multiples of π

Or could be written as: except at πk where k is an integer / / 2π

/ except odd multiples of kπ/2

Or could be written as: except at π/2 + πk / / 2π

/ except at multiples of π

Or could be written as: except at πk where k is an integer / / π

/ [-1,1] / [-π/2, π/2] / N/A

/ [-1,1] / [0, π] / N/A

/ / (-π/2, π/2) / N/A