Question

If the function y = sinx is transformed to y = 3 sine (two-thirds x), how do the amplitude and period change?

Answer 1

Change in Amplitude is 2

Change in Period is π

Transforming sin(x) to $3sin(\frac{2x}{3})$

y = a(sin(bx+c)) + d

Where, a is Amplitude and $\frac{2}{b}$π is period

Amplitude of sin(x) =1

Period of sin(x) = 2π

Amplitude of 3sin($\frac{2x}{3}$) = 3

Period of 3sin($\frac{2x}{3}$) = $\frac{2}{\frac{2}{3}}$*π = 3π

Change in Amplitude = 3sin($\frac{2x}{3}$) - sin(x)

                                    = 3 - 1

                                    = 2

Change in Period = 3sin($\frac{2x}{3}$) - sin(x)

                              = 3π - 2π

                               = π

To learn more about Amplitudes and Periods visit:

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