Phase Shift Quiz: Phase Shift as a Horizontal Translation of Sine and Cosine Graphs

  • 11th Grade
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| Attempts: 11 | Questions: 20 | Updated: Dec 17, 2025
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1) In y = cos(x − C), positive C shifts right.

Explanation

Subtracting a positive constant moves the graph right.

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About This Quiz
Phase Shift Quiz: Phase Shift As A Horizontal Translation Of Sine and Cosine Graphs - Quiz

How do horizontal shifts affect sine and cosine graphs? In this quiz, you’ll explore how phase shifts translate wave patterns along the x-axis and change the timing of peaks, troughs, and midline crossings. You’ll interpret equations, compare graphs, and see clearly how shifting inputs moves the entire curve. By working... see morethrough structured examples, you’ll build strong intuition for understanding transformations and predicting how phase affects real-world periodic motion.
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2) What does a phase shift represent for sine and cosine functions?

Explanation

Phase shift moves the graph left or right without altering amplitude or period.

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3) Select graphs shifted left relative to y = sin(x).

Explanation

Adding inside shifts left.

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4) If y = cos(x + π/2), what happens to y = cos(x)?

Explanation

Positive inside shift moves the graph left π/2.

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5) Which of these has no phase shift?

Explanation

The basic function y = sin(x) starts at the origin and has no shift.

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6) Select all functions shifted π/3 units right from y = sin(x).

Explanation

The (x − a) form shifts right by a units.

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7) Adding a constant C inside sin(x + C) shifts the graph to the left.

Explanation

Adding a constant inside shifts the graph left because input decreases by C to keep the same value.

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8) Sine shifted right π/3 is represented by:

Explanation

Right shift by π/3 uses subtraction: sin(x − π/3).

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9) Sine and cosine are phase-shifted versions of each other.

Explanation

cos(x) = sin(x + π/2); cosine leads sine by π/2.

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10) What x-value does y = cos(x − π/2) start its cycle?

Explanation

Shifting right π/2 means start at x = π/2.

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11) Phase shift of y = sin(bx − C) is C/b.

Explanation

Set bx − C = 0 → x = C/b, giving horizontal shift.

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12) General form of shifted sine: ____.

Explanation

A is amplitude, B affects period, C is phase shift, D is vertical shift.

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13) For y = sin(2x − π/2), select correct facts.

Explanation

Amplitude=1, Period=π, shift=π/4 right, frequency=2.

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14) To shift y = sin(x) left π/2, write it as ____.

Explanation

Adding π/2 shifts sine graph π/2 left.

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15) What is the phase shift of y = 3cos(4x + π)?

Explanation

Phase shift = −C/b = −π/4, so left π/4.

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16) For y = cos(2x − π/2), the phase shift is ____.

Explanation

Phase shift = C/b = (π/2)/2 = π/4 right.

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17) In y = sin(x − π/4), the graph shifts ____.

Explanation

Subtracting moves the graph right, so sin(x − π/4) shifts π/4 units right.

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18) Which transformations affect horizontal position of sine/cosine graphs?

Explanation

Phase, period, and y-reflection affect horizontal layout.

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19) Cos(x) = sin(x + ____).

Explanation

Sine and cosine differ by phase shift of π/2.

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20) Changing phase shift alters frequency.

Explanation

Phase shift only moves the graph; frequency depends on b.

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In y = cos(x − C), positive C shifts right.
What does a phase shift represent for sine and cosine functions?
Select graphs shifted left relative to y = sin(x).
If y = cos(x + π/2), what happens to y = cos(x)?
Which of these has no phase shift?
Select all functions shifted π/3 units right from y = sin(x).
Adding a constant C inside sin(x + C) shifts the graph to the left.
Sine shifted right π/3 is represented by:
Sine and cosine are phase-shifted versions of each other.
What x-value does y = cos(x − π/2) start its cycle?
Phase shift of y = sin(bx − C) is C/b.
General form of shifted sine: ____.
For y = sin(2x − π/2), select correct facts.
To shift y = sin(x) left π/2, write it as ____.
What is the phase shift of y = 3cos(4x + π)?
For y = cos(2x − π/2), the phase shift is ____.
In y = sin(x − π/4), the graph shifts ____.
Which transformations affect horizontal position of sine/cosine...
Cos(x) = sin(x + ____).
Changing phase shift alters frequency.
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