Question

What is the period of y=−5 cos( 8 π ​ x)+3? Give an exact value. units PLEASE MAKE IT QUICK

Answer 1

Answer:

Maximum/Minimum Value:  (0,−2)   is a local minima (1/8,8)  is a local maxima

Explanation: Use the derivative to find the maximum and minimum

Answer 2

Answer:

Period = ¹/₄

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

• A = amplitude (height from the mid-line to the peak)
• 2π/B = period (horizontal distance between consecutive peaks)
• C = phase shift (horizontal shift - positive is to the left)
• D = vertical shift

Given function:

$y=-5 \cos (8 \pi x)+3$

Comparing the given function with the standard form:

• A = 5
• B = 8π
• C = 0
• D = 3

$\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}$

Therefore, the period of the given function is ¹/₄.

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