Question

quiz 5: trig, exponential & logarithmic functions
6 points possible answered: 3/6
question 4
state the period, amplitude, phase shift, and vertical shift of the function.
$y = -\sin\left(x - \frac{\pi}{2}\
ight)$
period:
amplitude:
phase shift:
vertical shift:
question help: video ebook

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Explanation:

Step1: Recall the general form of a sine function

The general form of a sine function is \(y = A\sin(B(x - C))+D\).
For the function \(y = -\sin(x-\frac{\pi}{2})\), we have \(A=- 1\), \(B = 1\), \(C=\frac{\pi}{2}\), \(D = 0\).

Step2: Calculate the period

The formula for the period of a sine function \(y = A\sin(B(x - C))+D\) is \(T=\frac{2\pi}{|B|}\).
Since \(B = 1\), then \(T=\frac{2\pi}{|1|}=2\pi\).

Step3: Calculate the amplitude

The formula for the amplitude of a sine function \(y = A\sin(B(x - C))+D\) is \(|A|\).
Since \(A=-1\), then \(|A| = 1\).

Step4: Calculate the phase - shift

The formula for the phase - shift of a sine function \(y = A\sin(B(x - C))+D\) is \(C\).
Since \(C=\frac{\pi}{2}\), the phase - shift is \(\frac{\pi}{2}\) units to the right.

Step5: Calculate the vertical - shift

The formula for the vertical - shift of a sine function \(y = A\sin(B(x - C))+D\) is \(D\).
Since \(D = 0\), there is no vertical shift.

Answer:

Period: \(2\pi\)
Amplitude: \(1\)
Phase Shift: \(\frac{\pi}{2}\) units to the right
Vertical Shift: \(0\)