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What is the amplitude of y=-3cos(pi x+2)-6? ◻ units

What is the amplitude of y=−3cos⁡(πx+2)−6? y=-3 \cos (\pi x+2)-6 ? \newline□ \square units

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Full solution

Q. What is the amplitude of y=−3cos⁡(πx+2)−6? y=-3 \cos (\pi x+2)-6 ? \newline□ \square units
  1. Identify coefficient: Identify the coefficient in front of the cosine function, which represents the amplitude. The coefficient is −3-3.
  2. Calculate amplitude: The amplitude is the absolute value of the coefficient, because amplitude is always positive.\newlineSo, the amplitude is ∣−3∣=3|-3| = 3.
  3. Verify correctness: Check if the calculation is correct and if it makes sense in the context of the problem.\newlineThe amplitude of a cosine function is indeed the absolute value of its coefficient, and 33 is the correct absolute value of −3-3.

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