Question

hich function is the same as y = 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2? y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2 y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2

Answer 1

Answer:

B) y = -3 sin(2(x + π/4)) - 2

Step-by-step explanation:

Which function is the same as y = 3 cos(2 (x + π/2)) - 2

A)  y = 3 sin(2(x + π/2)) - 2

B) y = -3 sin(2(x + π/4)) - 2

C) y = 3 cos(2 (x + π/4)) - 2

D) y = -3 cos(2 (x + π/2)) - 2

y = 3 cos(2 (x + π/2)) - 2

Sine and cosine have the following relationship:

cos(θ) = sin (π/2 - θ)

y = 3 cos(2 (x + π/2)) - 2

⇒ y = 3 cos(2x + π) - 2

Let θ = 2x + π, therefore using Sine and cosine have the following relationship:

cos(2x + π) = sin (π/2- (2x + π))

= sin (π/2 - 2x - π)

= sin (-2x - π/2)

= sin (-2(x + π/4))

but sin(-θ) = -sin (θ)

Therefore:

sin (-2(x + π/4)) = -sin (2(x + π/4))

⇒ - sin (2(x + π/4)) = cos(2x + π)

y = 3 cos(2x + π) - 2 = 3[ - sin (2(x + π/4))] -2

y = -3 sin (2(x + π/4)) -2