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Find the perioa

equation.
llowing
y = 2 cos(5x + 3) - 6
77
Period = [2]T
Give your answer in simplest form.

Find the perioa equation. llowing y = 2 cos(5x + 3) - 6 77 Period = [2]T Give your-example-1
User ABiscuit
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1 Answer

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Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

User Shahzin KS
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