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3.02 Transformations of trigonometric functions

Adaptive
Worksheet

Interactive practice questions

How does the graph of $y=3\cos x$y=3cosx differ from the graph of $y=\cos x$y=cosx?

Select the two correct options.

The amplitude of $y=3\cos x$y=3cosx is $3$3 times greater than the amplitude of $y=\cos x$y=cosx.

A

The period of $y=3\cos x$y=3cosx is greater than the period of $y=\cos x$y=cosx.

B

The maximum value of $y=3\cos x$y=3cosx is $3$3 times greater than the maximum value of $y=\cos x$y=cosx.

C

$y=3\cos x$y=3cosx is a reflection of $y=\cos x$y=cosx about the $x$x-axis.

D
Medium
1 min

Determine the equation of the graphed function given that it is of the form $y=a\sin x$y=asinx or $y=a\cos x$y=acosx, where $x$x is in degrees.

Medium
1 min

Determine the equation of the graphed function given that it is of the form $y=a\sin x$y=asinx or $y=a\cos x$y=acosx.

Medium
< 1 min

State the amplitude of $y=-4\sin x$y=4sinx.

Medium
< 1 min
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Outcomes

T.GT.1b

Determine the domain and range, amplitude, period, and asymptote locations for a trigonometric function, given a graph or an equation.

T.GT.1c

Describe the effects of changing the parameters (A, B, C, or D in the standard form of a trigonometric equation) on the graph of the function using graphing technology.

T.GT.1d

Sketch the graph of a transformed sine, cosine, and tangent function written in standard form by using transformations for at least a two-period interval, including both positive and negative values for the domain.

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