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.
$y = -\cos\left(x - \frac{\pi}{2}\
ight)$
period:
amplitude:
phase shift:
vertical shift:
question help: video ebook

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Explanation:

Step1: Recall the general form of a cosine function

The general form of a cosine function is \(y = A\cos(B(x - C))+D\), where:

• Amplitude \(=|A|\)
• Period \(=\frac{2\pi}{|B|}\)
• Phase - shift \(=C\)
• Vertical - shift \(=D\)

For the function \(y =-\cos(x-\frac{\pi}{2})\), we can rewrite it as \(y =(- 1)\cos(1\times(x-\frac{\pi}{2}))+0\)

Step2: Calculate the amplitude

Here \(A=-1\). Using the formula for amplitude \(|A|\), we have \(| - 1|=1\)

Step3: Calculate the period

Here \(B = 1\). Using the formula for period \(\frac{2\pi}{|B|}\), we get \(\frac{2\pi}{|1|}=2\pi\)

Step4: Calculate the phase - shift

Here \(C=\frac{\pi}{2}\). So the phase - shift is \(\frac{\pi}{2}\) units to the right (since \(C>0\))

Step5: Calculate the vertical - shift

Here \(D = 0\)

Answer:

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