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Test 2 - Math 2412 Name___________________________________
Chapter 4 and 5
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Use a vertical shift to graph the function.
6) y = -3 sin 2x +
The point P(x, y) on the unit circle that corresponds to a
real number t is given. Find the value of the indicated
trigonometric function at t.
5
2 6
,Find csc t.
1)
7
7
Solve the problem.
2) What is the domain of the sine function?
Determine the phase shift of the function.
1
3) y = -5 sin x 2
2
Determine the amplitude or period as requested.
1
4) Period of y = -5 cos x
2
Graph the function.
x
7) y = 4 tan
2
Graph the function.
2
5) y = - cos 2x +
3
2
8) y = 2 cot x +
1A
4
2
-2
Solve the equation on the interval [0, 2 ).
3
18) cos 2x =
2
Use the graph to obtain the graph of the reciprocal
function. Give the equation of the function for the graph
that you obtain.
9) y = 3 cos 2 x
Find the exact value of the expression.
19) cos (160°) cos (40°) + sin (160°) sin (40°)
Use the given information to find the exact value of the
expression.
3
2
20) sin = , lies in quadrant II, and cos = ,
5
5
lies in quadrant I
Use a half-angle formula to find the exact value of the
expression.
21) sin 22.5°
Find the exact value of the expression.
2
10) cos-1 2
Solve the equation on the interval [0, 2 ).
22) sin 3x = 0
11) tan-1 0
Use the given information to find the exact value of the
trigonometric function.
3
lies in quadrant IV
Find
23) sin = - ,
5
Use a sketch to find the exact value of the expression.
3
12) cos tan-1
8
sin
Use a right triangle to write the expression as an
algebraic expression. Assume that x is positive and in the
domain of the given inverse trigonometric function.
x2 + 4
)
13) tan(sec -1
x
(sin x + cos x)2
=?
1 + 2 sin x cos x
15)
sin x + cos x cos x - sin x
=?
sin x
cos x
2
.
Use the given information to find the exact value of the
expression.
20
, lies in quadrant IV
Find sin 2
24) cos =
29
.
Complete the identity.
14)
Find cos ( - ).
Express the product as a sum or difference.
25) sin 7x sin 3x
The point P(x, y) on the unit circle that corresponds to a
real number t is given. Find the value of the indicated
trigonometric function at t.
3
2 10
,Find csc t.
26)
7
7
Solve the equation on the interval [0, 2 ).
16) sin2 x + sin x = 0
Find the exact value of the trigonometric function. Do not
use a calculator.
Solve the equation on the interval [0, 2 ).
17) (tan x + 1) (sin x + 1) = 0
27) -tan
2
4
+ 19
Use even and odd properties of the trigonometric
functions to find the exact value of the expression.
28) cos (-150°)
34) y = 2 sec
x
3
Sin t and cos t are given. Use identities to find the
indicated value. Where necessary, rationalize
denominators.
3
2 10
. Find tan t.
29) sin t = , cos t =
7
7
Use a calculator to find the value of the trigonometric
function to four decimal places.
30) cot
10
35) y = 6 csc x +
Determine the phase shift of the function.
1
31) y = 5 sin x 4
4
2
Graph the function.
32) y = -2 sin (3 x + 2)
Find the exact value of the expression, if possible. Do not
use a calculator.
36) cos-1 cos
33) y = -tan x +
6
Use a sketch to find the exact value of the expression.
3 73
37) cot sin-1
73
2
Use a right triangle to write the expression as an
algebraic expression. Assume that x is positive and in the
domain of the given inverse trigonometric function.
x2 + 4
)
38) sin(sec-1
x
Use substitution to determine whether the given x-value
is a solution of the equation.
4
2 3
, x=
39) sin x = 3
3
3
Find all solutions of the equation.
40) 5 sin x - 5 3 = 3 sin x- 4 3
Solve the equation on the interval [0, 2 ).
2
41) cos 2x =
2
42) cos2 x + 2 cos x + 1 = 0
43) sin2 x - cos2 x = 0
Solve the equation on the interval [0, 2 ).
44) tan2 x sin x = tan2 x
Solve the equation on the interval [0, 2 ).
45) tan 2x - tan x = 0
46) cos x +
4
- cos x -
4
=1
Use a calculator to solve the equation on the interval [0, 2
). Round the answer to two decimal places.
47) sin x = -0.37
Use a calculator to solve the equation on the interval [0, 2
). Round to the nearest hundredth of a radian.
48) cos 2x - cos x = 0
Find the exact value of the expression, if possible. Do not
use a calculator.
49) cos-1 cos -
6
4
Answer Key
Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 -
1) -
8)
7 6
12
2) all real numbers
3) units to the right
4) 4
5)
9) y = 3 sec 2 x
6)
10)
3
4
11) 0
8 73
12)
73
7)
13)
2
x
14) 1
15) sec x csc x
3
16) 0, ,
2
17)
18)
12
19) -
5
,
4
,
2
,
4
11
13 23
,
,
12 12
12
1
2
20)
-8 + 3 21
25
21)
1
2
2-
2
Answer Key
Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 -
22) 0,
3
,
23)
10
10
24) -
840
841
25)
34)
2
4
5
, ,
,
,2
3
3
3
1
(cos 4x - cos 10x)
2
26) -
7 10
20
27) -1
28) 29)
3
2
35)
3 10
20
30) 3.0777
31) units to the right
32)
36)
33)
6
37)
8
3
38)
2 x2 + 4
x2 + 4
39) No
40) x =
41)
8
4
+ 2n or x =
,
7
9
15
,
,
8
8
8
,
3
5
7
,
,
4
4
4
42)
43)
3
44) 0,
45) 0,
46)
4
,
4
47) 3.52, 5.90
48) 0, 2.09, 4.19
6
3
+ 2n
Answer Key
Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 -
49)
6
7