Multiple Choice
Describe the phase shift for the following function:
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10. Graphing Trigonometric Functions
Phase Shifts
Multiple Choice
Describe the phase shift for the following function:
A
to the right
B
to the left
C
to the right
D
to the left
Verified step by step guidance1
Identify the general form of the cosine function with a phase shift: y = cos(bx - c). In this case, the function is y = cos(5x - \(\frac{\pi}{2}\)).
Determine the phase shift by using the formula \(\frac{c}{b}\), where c is the horizontal shift and b is the coefficient of x. Here, c = \(\frac{\pi}{2}\) and b = 5.
Calculate the phase shift: \(\frac{\pi}{2}\) divided by 5, which simplifies to \(\frac{\pi}{10}\).
Determine the direction of the phase shift. Since the expression inside the cosine function is (5x - \(\frac{\pi}{2}\)), the phase shift is to the right.
Conclude that the phase shift for the function y = cos(5x - \(\frac{\pi}{2}\)) is \(\frac{\pi}{10}\) to the right.
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