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How do you find the amplitude, period, and shift for #y= 4 sin(theta/2)#?

Answer 1

Anna Andrews

#y = 4sin (x/2)#

Amplitude: (-4, 4) Shift: 0 Period of sin x is #2pi#, then period of #x/2# is #4pi.#

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Answer 2

Josiah Anderson

For the function y = 4 sin(theta/2), the amplitude is 4, the period is 4π, and there is no horizontal shift.

The amplitude of a sine function determines the maximum displacement from the midline. In this case, the amplitude is 4, meaning the graph of the function will oscillate between -4 and 4.

The period of a sine function is the distance between two consecutive peaks (or troughs) of the graph. The period can be calculated using the formula 2π/b, where b is the coefficient of theta in the function. Here, b = 1/2, so the period is 2π / (1/2) = 4π.

Since there is no horizontal shift, the function is not shifted to the left or right on the graph. Therefore, the shift is 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.