Compute values analytically (by “hand”) if possible, for remaining problems use

calculator. (a) and (b), may involve square roots so use them in your answers.

(a) State the exact value of sin(120).

(b) State the exact value of tan(2π/3).

(c) cos(83)

(d) sec(83)

(d) sin(5π/8)

2. (10 pts) Given a right triangle having an acute angle of 15and hypotenuse of length 5.0, find the

measurement of the other angle and the other sides. Show work. Be sure to clearly identify which of your

answers is the length of the side adjacent to and which is the length of the side opposite , as well as stating

the measure of the other acute angle. Report the lengths rounded to one decimal place.

For #2, you are welcome to use the following template if you like – just edit the labels (“___”) as desired.

______

________

________

______

________

3. (10 pts) Suppose that the point (√7, −3) lies on the terminal side of an angle in standard position.

Find the exact values of the six trigonometric functions of . Work optional. Rationalize

denominators as appropriate.

sin( ) =

cos( ) =

tan( ) =

csc( ) =

sec( ) =

cot( ) =

4. (12 pts) A person is sitting on the ground between the Acme and Baker buildings. The person is 34

feet from the Acme building. The Baker building is 58.2 feet tall. From the person’s point of view, the

angle of elevation to the top of the Acme building is 63 and the angle of elevation to the top of Baker

building is 45. Show work in answering the following questions:

(a) How tall is the Acme building?

(b) How far apart are the two buildings?

Report the values to the nearest tenth of a foot.

Acme

Baker

56’

62.4 45

34’

5. (8 pts) Use a sum or a difference identity to find the exact value of cos(105). Show work.

6. (12 pts) Given that sin( ) = 4/7 for an angle in Quadrant II, find the exact values of each of the

following. Show work. Rationalize denominators as appropriate.

(a) cos( )

(b) sin(2 )

(c) cos(2 )

7. (8 pts) Consider = 3 (5 − )

2

(a) State the amplitude.

(b) State the period.

(c) State the phase shift.

(no explanation required)

8. (9 pts) State all of the exact solutions of the equation sin(2x) = 1/2 in the interval [0, 2).

(work optional)

9. (9 pts) Prove the identity sec cos tan sin .

HINT: Rewrite each side of the expression using sines and cosines, simplify and apply a Pythagorean identity.

Show work.

10. (12 pts) (work optional)

(a) Find the exact value of arcsec(2).

√3

(b) Find the exact value of

tan (arcsin ( 2 )).

(c) Find the exact value of

arcsin (sin

(d) Find the exact value of

arccos (tan

3

2

).

5

4

).