Download Math-180-Exam #3 (Trigonometry Functions) Practice Exam

Math-180-Exam #3 (Trigonometry Functions)
Practice Exam
Name___________________________________
Date: ____________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered. Box your final answer and write your
answers in the answer column when possible.
Convert the angle in degrees to radians. Express answer as a multiple of .
1) - 480°
Convert the angle in radians to degrees.
43
2)
18
1)
2)
Convert the angle in radians to degrees. Round to two decimal places.
4
radians
3)
7
Draw the angle in standard position.
7
4) 6
3)
4)
Find a positive angle less than 360° or 2 that is coterminal with the given angle.
5) -44°
Solve the problem.
6) A lawn sprinkler rotates through an angle of 135° and projects water over a distance of 24
feet. What is the area of the lawn watered by the sprinkler? Express the answer in terms of
and then round to two decimal places.
5)
6)
Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the
given angle. Give an exact answer with a rational denominator.
7) Find csc .
7)
7
8
Use an identity to find the value of the expression. Do not use a calculator.
8) sin2 40° + cos2 40°
9) sec2 35° - tan2 35°
8)
9)
1
Solve the problem.
10) A surveyor is measuring the distance across a small lake. He has set up his transit on one
side of the lake 110 feet from a piling that is directly across from a pier on the other side of
the lake. From his transit, the angle between the piling and the pier is 60°. What is the
distance between the piling and the pier to the nearest foot?
Find the exact value of the expression. Do not use a calculator.
11) 1 - tan2 60° + csc2 30°
A point on the terminal side of angle
1 1
12) (- , ) Find cos .
3 2
=-
2
, tan
3
>0
12)
Find sec .
13)
14)
Find the reference angle for the given angle.
15) 103°
16) -
11)
is given. Find the exact value of the indicated trigonometric function of .
Find the exact value of the indicated trigonometric function of .
4
Find sin .
13) cos = , tan < 0
9
14) sin
10)
15)
13
12
16)
Use reference angles to find the exact value of the expression. Do not use a calculator.
-11
17) cot
6
18) csc 660°
17)
18)
The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated
trigonometric function at t.
33 4
,
Find cos t.
19) 19)
7 7
Use the unit circle to find the value of the trigonometric function.
20) sec
20)
6
Use even and odd properties of the trigonometric functions to find the exact value of the expression.
21) cos -
21)
4
2
22) cos (-150°)
22)
Graph the function and y = cos x in the same rectangular system for 0
23) y = 2 cos x
Determine the amplitude or period as requested.
1
24) Amplitude of y = -2 cos x
3
x
2 .
23)
24)
25) Period of y = cos 5x
25)
Determine the phase shift of the function.
26) y = -5 cos (8x + )
26)
27) y = 4 sin (4 x + 3)
27)
Graph the function.
28) y = 2 cos 3x
28)
3
Use a vertical shift to graph the function.
1
29) y = -3 sin x - 2
2
29)
Find an equation for the graph.
30)
30)
Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest tenth of
a degree.
31) A = 38°, b = 42.9
31)
Solve the problem.
32) A straight trail with a uniform inclination of 15° leads from a lodge at an elevation of 500
feet to a mountain lake at an elevation of 9600 feet. What is the length of the trail (to the
nearest foot)?
Complete the identity.
33) sec4 x + sec2 x tan2 x - 2 tan4 x = ?
32)
33)
4
34)
(tan x + 1)(tan x + 1) - sec2 x
=?
tan x
34)
Verify the identity.
35) (1 + tan2 u)(1 - sin2 u) = 1
35)
5
Answer Key
Testname: MATH-180-E3-PRACTICE
1) -
8
radians
3
2) 430°
3) 102.86°
4)
5) 316°
6) 216
678.58sq ft
113
7)
8
8)
9)
10)
11)
1
1
191 feet
2
2 13
12) 13
13) -
65
9
14) -
3 5
5
15) 77°
16)
12
3
2 3
18) 3
17)
19) -
33
7
20)
2 3
3
21)
2
2
22) -
3
2
6
Answer Key
Testname: MATH-180-E3-PRACTICE
23)
24) 2
2
25)
5
26)
27)
8
units to the left
3
units to the left
4
28)
29)
30) y = 5 sin
1
x
3
31) B = 52°, a = 33.5, c = 54.4
7
Answer Key
Testname: MATH-180-E3-PRACTICE
32) 35,160 feet
33) 3 sec4 x - 2
34) 2
35) (1 + tan2 u)(1 - sin2 u) = sec2 u · cos2 u =
1
· cos2 u = 1
cos2 u
8