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practice test 4-1316-Fall-2010
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression in degrees without using a calculator or table.
1
1) arcsin - 2
A) -30°
2) sec -1 B) 300°
D) 30°
2)
2
A) 135°
B) 45°
Find the exact value for x in the interval 0, 3) tan (x) = A)
C) 315°
1)
C) 225°
D) 30°
π
that satisfies the equation.
2
3
3
π
6
3)
B)
π
4
C)
π
3
D)
π
2
Find the exact value of the composition.
4) tan (2 tan-1 (2))
2
A)
3
4)
4
B)
3
2
C) - 3
4
D) - 3
Find an equivalent algebraic expression for the composition.
5) sin (arccot (x))
x2
A)
x2 + 1
6) sec (arccos (x))
1
A)
x
5)
B)
1
x2 + 1
C)
x
x2 + 1
1
D)
2
x + 1
6)
1
B)
x2
C) x
D)
x
Find all real numbers that satisfy the equation.
7) 2 sin x = 3
7)
π
2π
A) x x = + 2kπ or x = + 2kπ
3
3
π
B) x x = + kπ
3
π
5π
C) x x = + 2kπ or x = + 2kπ
6
6
π
D) x x = + kπ
6
1
8)
8) 2 cos x + 1 = 0
2π
4π
+ nπ or x = + nπ
A) x = 3
3
π
3π
B) x = + nπ or x = + nπ
2
2
3π
π
+ 2nπ
C) x = + 2nπ or x = 2
2
D) x = 2π
4π
+ 2nπ or x = + 2nπ
3
3
Solve the equation for x.
9) y = -5 sin 8x
1
y
A) x = arcsin 8
5
9)
y
-1
B) x = arcsin 5
8
1
-y
C) x = arcsin 8
5
1
-y
D) x = arcsin 5
8
10) y = 3 tan 2x - 1
1
A) x = arctan (3y + 3)
2
10)
B) x = 2 arctan (3y + 3)
y + 1
1
C) x = arctan 3
2
D) x = 2 arctan y + 1
3
Find the inverse of the function, and state the domain and range of the inverse function.
π
11) f(x) = 6 cos (2x) + 2 for 0 ≤ x ≤ 2
11)
1
x - 2
π
A) f-1 (x) = cos-1 ; domain = [-8, 8]; range = 0, 2
6
2
1
x - 2
B) f-1 (x) = cos-1 ; domain = [-4, 8]; range = 0, π
2
6
1
x - 2
π
C) f-1 (x) = cos-1 ; domain = [-4, 8]; range = 0, 2
6
2
1
x - 6
π
D) f-1 (x) = cos-1 ; domain = [-4, 8]; range = 0, 2
2
2
1
1
12) f(x) = 9 + tan (πx) for - ≤ x ≤ 2
2
12)
tan-1 (x - 9)
1 1
A) f-1 (x) = ; domain = (-∞, ∞); range = - , π
2 2
1 1
B) f-1 (x) = π tan-1 (x - 9); domain = (-∞, ∞); range = - , 2 2
tan-1 (x + 9)
1 1
C) f-1 (x) = ; domain = (-∞, ∞); range = - , π
2 2
D) f-1 (x) = tan-1 (x - 9)
π π
; domain = (-∞, ∞); range = - , π
2 2
2
Find all real numbers that satisfy the equation.
13) tan 4x = 0
13)
A) {x x = 2kπ}
kπ
B) x x = 4
C) {x x = kπ}
D) x x = π kπ
+ 12 12
Find all values of θ in [0°, 360°) that satisfy the equation.
1
14) cos θ = 2
A) {60°, 120°}
14)
B) {150°, 210°}
C) {210°, 330°}
D) {60°, 300°}
15) 2 sin 2θ - 3 = 0
15)
A) {60°, 150°, 240°, 300°}
B) {30°, 150°, 210°, 330°}
C) {60°, 120°, 240°, 300°}
D) {30°, 60°, 210°, 240°}
Find all real numbers in [0, 2π] that satisfy the equation.
16)
16)
2 cos (2x) = 1
π 7π 9π 15π
A) , , , 8
8
8 8
C) 0, π 3π 5π 7π
B) , , , 4 4
4
4
2π
4π
, π, 3
3
D) no solution
Solve the problem.
17) A coil of wire rotating in a magnetic field induces a voltage given by e = 20 sin πt π
- , where t is
4
2
17)
time in seconds. Find the smallest positive time to produce a voltage of 10 3.
A) 3.33π sec
B) 3 sec
C) 3.33 sec
D) 3π sec
Find all real numbers in the interval [0, 2 π) that satisfy the equation.
18) tan x + sec x = 1
5π
A)
4
18)
B) {0}
C)
19) 2 sin2 x = sin x
π 5π
A) 0, π, , 6 6
C)
π
4
D) No solution
19)
π 3π π 2π
B)
, , , 2 2 3 3
π 2π
, 3 3
D)
π 5π
, 6 6
C)
π 7π
, 4 4
20) cos2 x + 2 cos x + 1 = 0
A) {π}
20)
π 3π
, B)
2 2
3
D) {2π}
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
21) A water wheel rotates through the angle θ, the water level L behind the wheel changes
according to the equation
L = 1 - sin θ - 2 cos2 θ
21)
where L is measured in inches. Determine the values of θ for which the water level is zero.
Find the exact values. Do not use a calculator.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find all real numbers that satisfy the equation.
22) sin x = 1
22)
A) {x|x = π + 2kπ}
3π
B) x|x = + 2kπ
2
C) {x|x = 0 + 2kπ}
π
D) x|x = + 2kπ
2
4
Answer Key
Testname: PTEST4‐1316‐FALL2010
1) A
2) B
3) A
4) D
5) B
6) A
7) A
8) D
9) C
10) C
11) C
12) A
13) B
14) D
15) D
16) A
17) C
18) B
19) A
20) A
π 7π 11π
, 21) θ = , 6
2 6
22) D
5