Question

Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2?

Answer 1

The equation that is the same as y = 3 cos(2 (x + π/2)) - 2 is y = -3 sin (2(x + π/4)) -2

What is the equivalent sine equation?

We have the original equation as;

y = 3 cos(2 (x + π/2)) - 2

The sine and cosine functions are related by the formula;

cos(θ) = sin (π/2 - θ)

Hence;

y = 3 cos(2 (x + π/2)) - 2

y = 3 cos(2x + π) - 2

When θ = 2x + π, it follows that:

cos(2x + π) = sin (π/2- (2x + π))

= sin (-2(x + π/4))

Since

sin(-θ) = -sin (θ)

Then:

sin (-2(x + π/4)) = -sin (2(x + π/4))

So

sin (2(x + π/4)) = cos(2x + π)

Finally;

y = -3 sin (2(x + π/4)) -2

Learn more about equivalent equation:https://brainly.com/question/16905759

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