Effect of Adding a Constant to Sin/Cos Function (Leaving Cert Mathematics): Quizzes

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Effect of Adding a Constant to Sin/Cos Function
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What effect does adding a constant to y=sin⁡(x)y = \sin(x) or y=cos⁡(x)y = \cos(x) have on the graph?

Vertical shift

For y=sin⁡(x)+ky = \sin(x) + k where k>0k > 0, what happens to the graph?

Shifts upward by kk units

For y=cos⁡(x)+ky = \cos(x) + k where k<0k < 0, what happens to the graph?

Shifts downward by ∣k∣|k| units

What is the new midline for y=sin⁡(x)+ky = \sin(x) + k?

y=ky = k

What is the midline of y=sin⁡(x)+3y = \sin(x) + 3?

y=3y = 3

Which properties remain unchanged when adding a constant to y=sin⁡(x)y = \sin(x)?

Amplitude, period, and frequency

Does adding a constant to y=cos⁡(x)y = \cos(x) affect its amplitude?

No, amplitude remains the same

What is the period of y=sin⁡(x)+ky = \sin(x) + k?

2π2\pi

How does the graph of y=sin⁡(x)+2y = \sin(x) + 2 compare to y=sin⁡(x)y = \sin(x)?

Moved up by 2 units

What is the midline of y=cos⁡(x)−2y = \cos(x) - 2?

y=−2y = -2

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Special Angles & The Unit Circle

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The Basics

Special Angles & The Unit Circle

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Periodic Functions

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The Basics

Special Angles & The Unit Circle

Radians & Sectors

Periodic Functions

Solving Trig Equations

Trig Identities

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