Graphing Sine and Cosine Functions

A Grade 12 math worksheet on graphing sine and cosine functions, focusing on amplitude, period, phase shift, and vertical shift.

Grade 12 Math TrigonometryGraphing Sine and Cosine

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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.B.5CCSS.MATH.CONTENT.HSF.BF.B.3

Topics

TrigonometrySineCosineGraphingHigh School Math

8 sections · Free to use · Printable

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Graphing Sine and Cosine Functions

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Read each question carefully and follow the instructions to graph the trigonometric functions, identify their key features, or determine equations from given graphs.

For the function y = 3sin(2x - π/2) + 1, identify the following:

1. Amplitude:

2. Period:

3. Phase Shift:

4. Vertical Shift:

5. Graph one full period of the function y = 2cos(x + π/4) - 1 on the coordinate plane below. Label the amplitude, period, phase shift, and vertical shift.

6. Which of the following functions has an amplitude of 4, a period of π, and a phase shift of π/3 to the right?

y = 4sin(2x - 2π/3)

y = 4cos(x - π/3)

y = 4sin(2x + 2π/3)

y = 4cos(2x - π/3)

7. The of a sinusoidal function is half the distance between its maximum and minimum values.

8. A shift moves the entire graph horizontally.

9. The of y = A sin(Bx - C) + D is given by 2π/|B|.

10. The graph of y = sin(x) and y = cos(x - π/2) are identical.

True

False

11. Write the equation of a sine function with an amplitude of 3, a period of 4π, a phase shift of π to the left, and a vertical shift of 2 units up.