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Chapter 1 Review
Dual Credit Trigonometry – Meinke
Name: ____________________________________
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Evaluate each expression. Rationalize if necessary.
1.) sin 300
2.) tan (−1350)
3.) sin(5 π /6)
4.) cos 330 0
5.) csc(2 π/3)
6.) tan (−2 π/3)
7.) sec(1800 )
8.) cos (3 π/2)
9.) tan–1 ( −
12.) cos–1
3
)
3
1
2
15.) cos(cos–1 (
1
))
3
10.) sin–1 ( −
2
)
2
11.) sin–1 (–1)
13.) cos–1 ( −
1
)
2
14.) tan–1 (
16.) tan(tan–1 ( −
3
))
3
1
)
3
17.) cos(cos–1 2)
Find the quadrants for which:
18.) cotx < 0 and cos > 0
19.) sinx < 0 and tanx > 0
20.) sec < 0 and csc > 0
21.) Complete the following table.
Function
Domain
Range
−1
f(x) = sin x
−1
f(x) = cos x
−1
f(x) = tan x
22.) Find the value of each of the 6 trigonometric function EXACTLY (simplified radicals) for θ = 5π/3.
cos θ = ________
sec θ = _______
sin θ = ________
csc θ = _______
tan θ = ________
cot θ = _______
23.) Given sec θ = 3 and sin θ <0 find the EXACT (simplified radicals) values of the remaining trigonometric
functions.
sin θ = _____________
csc θ = ____________
cos θ = ____________
sec θ = 3
tan θ = _____________
cot θ = _____________
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Solve the following word problems.
24.) An 8-foot-long piece of 2-by-4 wood is used to prop up a fence. If the 2-by-4 makes a 40° angle with the
ground, how high above the ground is the point where the 2-by-4 contacts the fence?
25.) John views the top of a 458 foot water tower at an angle of elevation of 51º. How far away from the tower
is John standing?
26.) A person is standing 10 feet away from a 37 ft tree. What is the angle of elevation from the person to the
top of the tree? Express your answer in degrees.
27.) A bicycle wheel is rotating at a rate of 2 radians per second. There is a speck of dirt stuck to the middle of
one of the spokes, and another speck of dirt stuck to the wheel’s rim, located 8 inches from the center. Tell
which speck has a faster angular speed, and which speck has a faster linear speed. Explain and compute the
angular and linear speeds of both specks of dirt.
28.) Convert 250º to radians. Leave the answer in terms of π .
29.) Find the degree measure of
11π
9
.