Q.1 What is the period of the function y = sin(x)?
π
2π
π/2
4π
Explanation - The sine function completes one full cycle over an interval of 2π, making its period 2π.
Correct answer is: 2π
Q.2 What is the amplitude of y = 3sin(x)?
1
2
3
None
Explanation - The amplitude is the coefficient of sine or cosine, which here is 3.
Correct answer is: 3
Q.3 Which function has a period of π?
sin(x)
cos(x)
tan(x)
sec(x)
Explanation - The tangent function repeats every π units, unlike sine and cosine which repeat every 2π.
Correct answer is: tan(x)
Q.4 What is the range of y = cos(x)?
(-∞, ∞)
[-1, 1]
[0, 1]
(-1, ∞)
Explanation - The cosine function oscillates between -1 and 1, so its range is [-1, 1].
Correct answer is: [-1, 1]
Q.5 What is the maximum value of y = -2cos(x)?
2
-2
1
-1
Explanation - Since cosine ranges between -1 and 1, multiplying by -2 flips and stretches it, giving maximum value 2.
Correct answer is: 2
Q.6 What is the phase shift of y = sin(x - π/4)?
π/4 to the left
π/4 to the right
No shift
π/2 to the right
Explanation - A minus inside the function shifts the graph to the right, so sin(x - π/4) shifts π/4 to the right.
Correct answer is: π/4 to the right
Q.7 Which trigonometric function has vertical asymptotes?
sin(x)
cos(x)
tan(x)
none
Explanation - Tangent has vertical asymptotes at x = (2n+1)π/2.
Correct answer is: tan(x)
Q.8 What is the midline of y = sin(x) + 2?
y = 0
y = 2
y = 1
y = -2
Explanation - Adding +2 shifts the sine graph upward, so the midline is y = 2.
Correct answer is: y = 2
Q.9 What is the range of y = 2cos(x) - 1?
[-3, 1]
[-1, 3]
[0, 2]
[-2, 2]
Explanation - Cos(x) ranges from -1 to 1. Multiplying by 2 gives [-2, 2]. Subtracting 1 shifts it down to [-3, 1].
Correct answer is: [-3, 1]
Q.10 At which x-values does y = sin(x) cross the x-axis?
nπ
(2n+1)π/2
π/4
π/6
Explanation - Sine crosses the x-axis at multiples of π.
Correct answer is: nπ
Q.11 What is the period of y = cos(2x)?
2π
π
π/2
4π
Explanation - For y = cos(kx), the period is 2π/k. Here k=2, so period = π.
Correct answer is: π
Q.12 Which graph is symmetric about the origin?
y = sin(x)
y = cos(x)
y = sec(x)
y = cot(x)
Explanation - Sine is an odd function, so it is symmetric about the origin.
Correct answer is: y = sin(x)
Q.13 The graph of y = cos(x) is shifted π/2 units to the right. What function is obtained?
y = sin(x)
y = -sin(x)
y = cos(x)
y = -cos(x)
Explanation - cos(x - π/2) = sin(x).
Correct answer is: y = sin(x)
Q.14 Which function has a range of [0, ∞)?
y = sin(x)
y = cos(x)
y = tan^2(x)
y = tan(x)
Explanation - Squaring makes tangent nonnegative, so range is [0, ∞).
Correct answer is: y = tan^2(x)
Q.15 The vertical shift of y = sin(x) - 4 is:
Up 4
Down 4
Right 4
Left 4
Explanation - Subtracting 4 shifts the sine graph downward by 4 units.
Correct answer is: Down 4
Q.16 What is the minimum value of y = 1 + cos(x)?
0
-1
2
-2
Explanation - cos(x) ranges from -1 to 1, so 1 + cos(x) ranges from 0 to 2. Minimum = 0.
Correct answer is: 0
Q.17 The graph of y = sin(x) is reflected across the x-axis. Which function represents it?
y = cos(x)
y = -sin(x)
y = -cos(x)
y = sin(-x)
Explanation - Reflecting across the x-axis multiplies by -1, so sin(x) becomes -sin(x).
Correct answer is: y = -sin(x)
Q.18 What is the amplitude of y = -5cos(x)?
-5
0
5
1
Explanation - Amplitude is always the absolute value of the coefficient, so amplitude = 5.
Correct answer is: 5
Q.19 Which of these graphs does not have an amplitude?
y = sin(x)
y = cos(x)
y = tan(x)
y = -sin(x)
Explanation - Tangent is unbounded, so amplitude is undefined.
Correct answer is: y = tan(x)
Q.20 What is the period of y = tan(3x)?
π
π/3
2π
2π/3
Explanation - The period of tan(kx) is π/k. Here k=3, so period = π/3.
Correct answer is: π/3
Q.21 Where are the asymptotes of y = cot(x)?
x = nπ
x = (2n+1)π/2
x = nπ/2
x = nπ/3
Explanation - Cotangent is undefined at multiples of π, so vertical asymptotes occur at x = nπ.
Correct answer is: x = nπ
Q.22 Which trigonometric function is even?
sin(x)
tan(x)
cos(x)
csc(x)
Explanation - Cosine is an even function, symmetric about the y-axis.
Correct answer is: cos(x)
Q.23 The graph of y = sin(x) is shifted upward by 3. What is its midline?
y = 0
y = 1
y = 3
y = -3
Explanation - Adding +3 shifts the entire sine graph up, so midline = y = 3.
Correct answer is: y = 3
Q.24 What is the range of y = sec(x)?
[-1, 1]
(-∞, -1] ∪ [1, ∞)
(0, ∞)
(-∞, ∞)
Explanation - Since sec(x) = 1/cos(x), its values are outside [-1, 1].
Correct answer is: (-∞, -1] ∪ [1, ∞)
Q.25 Which function has a period of 2π but no amplitude?
sin(x)
cos(x)
tan(x)
csc(x)
Explanation - Cosecant has period 2π but is unbounded, so amplitude is undefined.
Correct answer is: csc(x)