Question

y=-2cos(1/4x- pi/2)

Find the horizontal shift of this problem.

Answer 1

The horizontal shift is 2π to the right

Step-by-step explanation:

Let us revise the transformation of the trigonometric function:

y = A sin[B(x + C)] + D, where

• Amplitude is A
• Period is 2π/B
• Phase shift is C (positive is to the left)
• Vertical shift is D

∵ $y=-2cos(\frac{1}{4}x-\frac{\pi }{2})$

- At first take $\frac{1}{4}$ as a common factor from the bracket

∵ $\frac{1}{4}x$ ÷ $\frac{1}{4}$ = x

∵ $\frac{\pi }{2}$ ÷ $\frac{1}{4}$ = 2π

∴ $y=-2cos[\frac{1}{4}(x-2\pi )]$

Compare the function by the form of the function above

∴ A = -2, B = $\frac{1}{4}$ , C = -2π and D = 0

∵ The horizontal shift (phase shift) is C ⇒ positive to left

- C is -2π, then the shift is to the right

∴ The horizontal shift is 2π to the right

The horizontal shift is 2π to the right

Learn more:

You can learn more about the trigonometric ratios in  

brainly.com/question/4924817

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