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).
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.
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 − )
(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).
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.
10. (12 pts) (work optional)
(a) Find the exact value of arcsec(2).
(b) Find the exact value of
tan (arcsin ( 2 )).
(c) Find the exact value of
(d) Find the exact value of