Math 1013: Precalculus II - Trig Test #2 Practice Questions
Questions
1. Match the function on the left with the sketch on the right (no work needs to be shown here, fill in directly on
this sheet).
y = − sec x matches graph
-6
-4
y
1.0
y
1.0
0.5
0.5
2
-2
-0.5
(A)
4
x
6
-6
-4
-2
-0.5
(B)
-1.0
-4
2
-2
4
x
6
-6
-4
-2 -2
-4
-6
-0.5
(C)
y=
sin x2
(D)
matches graph
y = cos(3x) + sin x matches graph
-4
(E)
-2 -2
-4
-6
2
4
6
x
-2
+ cos(20x) matches graph
-6
-4
(F)
1
2
4
x
6
-6
-4
(H)
-1.0
10
-2
-2
2
4
6
-2
-4
-6
y
8
6
4
2
20
-4
x
y
6
4
2
30
-6
2
-1.0
y
40
(I)
x
-0.5
-2
-0.5
(G)
6
-1
0.5
y =
4
0.5
y
1.0
x2
2
x
y
1.0
y
8
6
4
2
-6
6
y
8
6
4
2
0.5
-6
4
-1.0
y
y = − tan x matches graph
2
-6
2
4
6
x
(J)
-4
-2 -2
-4
-6
2
4
6
x
x
Math 1013: Precalculus II - Trig Test #2 Practice Questions
2. Answer True or False (no work needs to be shown here, fill in directly on this sheet):
sin(π/4) =
√1
2
............................................................................................ T
F
............................................................................................T
F
............................................................................................. T
F
Sine is an even function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
cos x exhibits damping as x → ∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
cos t → ∞ as t → ∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
√
cos(π/3) =
3
2
tan(π/6) =
1
2
y=
1
x2 +1
sin t =
1
cos t
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T
F
tan t has period π/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
tan t =
sin t
cos t
...............................................................................................T
F
csc t has a vertical asymptote at t = π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
y = cos(2x) + sin(4x) is periodic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
y = cos(2x) + sin(4x) is a sinusoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
y = 2 cos(4x) + sin(4x) is a sinusoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
The domain of y = sin θ is θ ∈ [−1, 1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
The range of y = −7 sin θ is y ∈ [−7, 7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T
F
3. Sketch the sinusoid y = −5 sin(2x + 7) − 6. Determine the Amplitude, Period, and Phase Shift of the sinusoid.
Note: This one is a bit trickier than some that we have done–you might consider drawing intermediate sketches of
y = 5 sin(2x + 7) and y = −5 sin(2x + 7) to help you accurately sketch the final sinusoid.
4. Sketch the sinusoid y = 3 sin(π(2x + 1)). Determine the Amplitude, Period, and Phase Shift of the sinusoid.
Clearly label the location of a local minimum on your sketch.
√
5. Solve tan t = − 3 for all values of t.
6. Solve sec t =
√2
3
for all values of t.