Shears Math 122
T2 Sp12
sec. 6.5 – 7.4
Name _________________________________
Show all work in the space provided. Answers without work may receive reduced credit. There should
be no trig functions in your final answer. When exact answers are not called for, give answers accurate
to the thousandths place. Place answers in the blanks when provided. Answers should be simplified,
except you do not need to rationalize denominators. Formulas are on the last page.
(3 pts)
1.) Use the space below each graph to label it with the corresponding trigonometry function.
(8 pts)
2.) Identify the requested characteristics for the graph of the cosine function below.
Amplitude = ______________
Period = __________________
Vertical Shift = ____________
Phase Shift = ______________
(2 pts)
3.) Circle the equation that generates the graph indicated by the darker curve at the left.
y = |x| cos x
y = |x| sin x
y = x cos x
y = x sin x
(7 pts)
4.) Find the exact equation of a sine function with a phase shift of -1, a period of 4, amplitude of 7, and
a vertical shift of 3.
__________________________________
(8 pts)
5.) Let h(x) = f(x) + g(x) where f and g are depicted on the graph below. Draw h(x) on the same grid. Be
sure and extend your drawing all the way to both edges of the grid.
(7 pts)
6.) Evaluate cos (γ + 90°) exactly, if you know that sin γ =
5
.
7
(7 pts)
7.) Use a trig substitution to get the following expression in terms of one trig function and then factor the
expression: sec2x + 5tan x + 5
_______________________________
(8 pts)
1 − sin x
1 + sin x
8.) Prove the identity: ( sec x − tan x ) = by working each side independently or manipulating
2
just one side until it looks like the other side. Show every step so I know exactly what you did.
(11 pts)
9.) Let θ ∈(−270°, −180°) be a standard angle with sin θ = 1/3. Evaluate cos θ and sin (θ/2) exactly.
(3 pts) cos θ = ___________________
(8 pts) sin (θ/2) = __________________
(6 pts)
10.) Let x = 4sin β where β is an acute angle. Evaluate tan β in terms of x with no trig functions in your
answer.
tan β = __________________
(6 pts)
11. Use your calculator to get a decimal approximation to each of the following:
sin-1(¼) = _______________
(6 pts)
arcsec(3) = _____________
arccsc ( − 2 ) = __________
arccot( − 3 ) = __________
12.) Evaluate exactly:
cos-1(-1) = _________
(6 pts)
cot-1(3) = _____________
13.) Evaluate sin-1(sin 3) exactly.
_________________
(4 pts)
14.) Evaluate csc(tan-1(2/3) ) exactly.
_________________
(5 pts)
15.) Evaluate
cos ( 2sin −1 15 )
exactly.
_______________
(6 pts)
16.) Evaluate
sin −1(cos 2π9 ) exactly.
_______________