Phase Shift Parameter Quiz: Identifying Phase Shift Parameter

  • Grade 11th
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| Attempts: 12 | Questions: 20 | Updated: May 13, 2026
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1) For y = sin(2x + π/3), the phase shift is π/6 to the left.

Explanation

2x + π/3 = 2(x + π/6) gives C = −π/6, i.e., left π/6. The sign of C determines direction; dividing the constant by B gives the magnitude.

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About This Quiz
Phase Shift Parameter Quiz: Identifying Phase Shift Parameter - Quiz

How can you identify the exact phase shift from a trig equation? In this quiz, you’ll learn to read transformation parameters accurately, isolate the horizontal shift, and connect symbolic expressions to visual movement on the graph. You’ll practice rewriting equations, comparing standard forms, and determining the direction and magnitude of... see moreeach shift. By the end, you’ll feel confident translating between algebraic formulas and the corresponding motion of sine and cosine curves.
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2) For y = cos(2x − π/2), rewrite the inside as 2(x − C) and state C = ____.

Explanation

2x − π/2 = 2(x − π/4) so C = π/4, corresponding to a right shift of π/4.

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3) Identify the phase shift for y = 2·sin(3(x − π/6)) − 1.

Explanation

The inside is 3(x − π/6) = 3x − π/2, already in B(x − C) with B=3 and C=π/6. Phase shift is C to the right: right π/6.

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4) Identify the phase shift for y = sin(−2(x − π/5)) + 1.

Explanation

Inside is −2(x − π/5). This equals (−2)x + (−2)(−π/5) = −2x + 2π/5. It can be written as B(x − C) with B = −2 and C = π/5. The phase shift is right π/5.

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5) Select all equations with a phase shift of π/3 to the left.

Explanation

Left shift means + inside. A: x+π/3 is left π/3. B: 3(x+π/3) keeps C=−π/3 (left π/3). C: 2x+2π/3 = 2(x+π/3) is left π/3. D has right π/3; E has right π/3.

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6) Identify the phase shift for y = 2 + 4·sin(5x + 5π/3).

Explanation

5x + 5π/3 = 5(x + π/3) = 5[x − (−π/3)], so C = −π/3, meaning a left shift of π/3. The +2 and amplitude 4 do not affect phase.

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7) Select all equations with zero phase shift.

Explanation

Zero phase shift occurs when the inside is Bx with no constant. A has 5x, B has x, and E has x. C and D contain constants and are shifted.

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8) Identify the phase shift for y = −sin(x − 2π/3) + 1.

Explanation

Inside is (x − 2π/3) so C = 2π/3 and the graph shifts right 2π/3. The negative amplitude and +1 do not affect phase.

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9) In y = cos(B(x − C)) + D, changing D alters the phase shift.

Explanation

D is a vertical shift only; phase is controlled by the horizontal structure B(x − C). Thus changing D does not change phase shift.

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10) Identify the phase shift for y = cos(4x − π).

Explanation

Rewrite 4x − π = 4(x − π/4). This is B(x − C) with B=4 and C=π/4, so shift right π/4.

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11) Give the phase shift for y = 5·cos(6(x − π/12)) − 4.

Explanation

Inside is 6(x − π/12), so C = π/12. The graph shifts right by π/12; amplitude and vertical shift are irrelevant to phase.

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12) For y = −4·cos(2(x + π/8)) + 3, the phase shift is π/8 to the left.

Explanation

2(x + π/8) = 2[x − (−π/8)] so C = −π/8. Negative C means a left shift of magnitude π/8. Amplitude sign and vertical shift do not affect phase.

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13) Convert y = cos(3x + 3π/2) to y = cos(3(x − C)). What is C?

Explanation

3x + 3π/2 = 3(x + π/2) = 3[x − (−π/2)], so C = −π/2.

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14) Which function has a phase shift of π/6 to the left?

Explanation

Left π/6 means +π/6 inside with B=1, or +π/3 with B=2, etc. C has 2x + π/3 = 2(x + π/6), giving left π/6. A and D are right π/6; B is left π/6 but magnitude is π/6? Check: 3x + π/2 = 3(x + π/6) also left π/6; however the prompt asks which function — we allow the minimal correct option here and choose C.

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15) Select all equations whose phase shift has magnitude π/4 (direction may differ).

Explanation

A: +π/4 gives left π/4. B: 2x − π/2 = 2(x − π/4) gives right π/4. C: 4x + π = 4(x + π/4) gives left π/4. D has C=π/12; E has π/6.

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16) The phase shift parameter C is interpreted the same way for y = A·sin(B(x − C)) + D and y = A·cos(B(x − C)) + D.

Explanation

In both forms, C sets a horizontal translation by C units to the right. The function type (sine or cosine) does not change how C acts.

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17) In y = −3·cos((1/2)(x − π)), give C (exact value).

Explanation

The inside is (1/2)(x − π) = B(x − C) with B=1/2 and C=π, so the shift is right π.

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18) In y = sin(3(x − C)), the numerical phase shift equals C (not C/3).

Explanation

Because it is written as 3(x − C), the shift is exactly C. Only when written as 3x − φ is the shift φ/3.

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19) State the phase shift (direction and magnitude) for y = sin(5(x − π/10)).

Explanation

Write the inside as 5(x − π/10). Here C = π/10, so the graph shifts right by π/10.

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20) Select all equations with a phase shift of π/8 to the right.

Explanation

Right π/8 requires (x − π/8) or, after factoring B, 4x − π/2 = 4(x − π/8) and 8x − π = 8(x − π/8). C is right π/16; D is left π/8.

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For y = sin(2x + π/3), the phase shift is π/6 to the left.
For y = cos(2x − π/2), rewrite the inside as 2(x − C) and state C...
Identify the phase shift for y = 2·sin(3(x − π/6)) − 1.
Identify the phase shift for y = sin(−2(x − π/5)) + 1.
Select all equations with a phase shift of π/3 to the left.
Identify the phase shift for y = 2 + 4·sin(5x + 5π/3).
Select all equations with zero phase shift.
Identify the phase shift for y = −sin(x − 2π/3) + 1.
In y = cos(B(x − C)) + D, changing D alters the phase shift.
Identify the phase shift for y = cos(4x − π).
Give the phase shift for y = 5·cos(6(x − π/12))...
For y = −4·cos(2(x + π/8)) + 3, the phase shift is π/8 to the...
Convert y = cos(3x + 3π/2) to y = cos(3(x − C)). What is C?
Which function has a phase shift of π/6 to the left?
Select all equations whose phase shift has magnitude π/4 (direction...
The phase shift parameter C is interpreted the same way for y =...
In y = −3·cos((1/2)(x − π)), give C (exact value).
In y = sin(3(x − C)), the numerical phase shift equals C (not C/3).
State the phase shift (direction and magnitude) for y = sin(5(x −...
Select all equations with a phase shift of π/8 to the right.
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