Download Math-180-Exam #4 (Chapter 7) Practice Exams

Math-180-Exam #4 (Chapter 7)
Practice Exams
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.
Use a sketch to find the exact value of the expression.
4
1) cos sin-1
5
1)
Complete the identity.
sin x cos x
+
=?
2)
cos x sin x
2)
Write the expression as the cosine of an angle, knowing that the expression is the right side of the formula for cos ( - )
with particular values for and .
3) cos (170°) cos (50°) + sin (170°) sin (50°)
3)
Complete the identity.
4) cos ( + ) cos ( - ) = ?
4)
Use the given information to find the exact value of the expression.
5
3
, lies in quadrant III, and cos = - , lies in quadrant II
5) tan =
12
5
Use the figure to find the exact value of the trigonometric function.
6) Find cos 2 .
Find sin ( + ).
5)
6)
5
4
3
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than
1.
7) 8 cos2 x
7)
Use a half-angle formula to find the exact value of the expression.
5
8) sin
12
Express the product as a sum or difference.
9) sin 7x cos 3x
8)
9)
1
Complete the identity.
10) sin 2x sin 5x cos 2x cos 5x = ?
10)
Express the sum or difference as a product.
11) cos 6x + cos 4x
11)
Complete the identity.
sin 3x + sin 9x
=?
12)
cos 3x + cos 9x
12)
Verify the identity.
cos x + cos y
x-y
= cot
13)
sin x - sin y
2
13)
Find all solutions of the equation.
14) 2 cos x - 1 = 0
14)
15) tan x sec x = -2 tan x
15)
Solve the equation on the interval [0, 2 ).
2
16) cos 2x =
2
16)
17) sin2 x + sin x = 0
17)
18) sin2 2x = 1
18)
Solve the equation on the interval [0, 2 ).
19) cos x + 2 cos x sin x = 0
19)
Solve the equation on the interval [0, 2 ).
11
11
- sin x =1
20) sin x +
6
6
20)
2
Answer Key
Testname: MATH-180-E4-F15-PRACTICE
1)
3
5
2) sec x csc x
3) cos (120°)
4) cos2 - sin2
5) -
33
65
6) -
7
25
7) 4 + 4 cos 2x
1
2+ 3
8)
2
9)
1
(sin 10x + sin 4x)
2
10)
cos2 3x - cos2 7x
4
11) 2 cos 5x cos x
12) tan 6x
13)
cos x + cos y
=
sin x - sin y
14) x =
3
15) x =
16)
19)
+ 2n or x =
3
3
cos
=
x-y
2
x-y
sin
2
= cot
x-y
2
+ 2n
+ 2n or x = n
7 9
15
,
,
8 8 8
8
,
17) 0, ,
18)
x-y
x+y
2 sin
cos
2
2
+ 2n or x =
3
x+y
x-y
cos
2
2
2 cos
4
2
,
,
3
2
3 5
7
,
,
4 4
4
6
,
2
,
11
6
20)
3