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What is the amplitude of y=-4cos(5x-9)-7 ? ◻ units

What is the amplitude of y=−4cos⁡(5x−9)−7 y=-4 \cos (5 x-9)-7 ?\newline□ \square units

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Full solution

Q. What is the amplitude of y=−4cos⁡(5x−9)−7 y=-4 \cos (5 x-9)-7 ?\newline□ \square units
  1. Amplitude Definition: The amplitude of a trigonometric function like y=Acos⁡(Bx−C)+Dy = A\cos(Bx - C) + D is the absolute value of the coefficient AA. This is because the amplitude represents the maximum distance from the function's midline (which is y=Dy = D) to its peak or trough.
  2. Identifying Coefficient AA: In the given function y=−4cos⁡(5x−9)−7y = -4\cos(5x - 9) - 7, the coefficient AA is −4-4. To find the amplitude, we take the absolute value of −4-4, which is 44.
  3. Calculating Amplitude: The amplitude of the function is therefore 44 units.

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