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
