a = vertical stretch, amplitude = |a| b = horizontal stretch, horizontal shrink if b>1, horizontal stretch…

a = vertical stretch, amplitude = |a| b = horizontal stretch, horizontal shrink if b>1, horizontal stretch if 0<b<1 c = horizontal shift / phase shift d = vertical shift, affects midline + range! check your understanding 1. a) graph y = - 3 cos x b) graph y = 2 sin(x - π/2) 2. determine the domain, range, period, and amplitude of y = 5 cos(1/2 x)+2 3. the equation for the graph below is given by y = a sin(bx)+c. find the values of a, which of the following equations is not equivalent to the other three? a) y = cos(x + π/2) b) y = sin(-x) c) y = sin(x + π) d) y = -cos(x)

a = vertical stretch, amplitude = |a| b = horizontal stretch, horizontal shrink if b>1, horizontal stretch if 0<b<1 c = horizontal shift / phase shift d = vertical shift, affects midline + range! check your understanding 1. a) graph y = - 3 cos x b) graph y = 2 sin(x - π/2) 2. determine the domain, range, period, and amplitude of y = 5 cos(1/2 x)+2 3. the equation for the graph below is given by y = a sin(bx)+c. find the values of a, which of the following equations is not equivalent to the other three? a) y = cos(x + π/2) b) y = sin(-x) c) y = sin(x + π) d) y = -cos(x)

Answer

Explanation:

Step1: Recall trigonometric identities

Use $\cos(x +\frac{\pi}{2})=-\sin(x)$ and $\sin(x+\pi)=-\sin(x)$.

Step2: Analyze option A

For $y = \cos(x+\frac{\pi}{2})$, by the co - function identity, $y=-\sin(x)$.

Step3: Analyze option B

$y=\sin(-x)=-\sin(x)$ (since $\sin(-\alpha)=-\sin(\alpha)$).

Step4: Analyze option C

$y = \sin(x+\pi)=-\sin(x)$ (using the angle - addition formula for sine or the unit - circle property).

Step5: Analyze option D

$y =-\cos(x)$ which is not equal to $-\sin(x)$.

Answer:

D. $y =-\cos(x)$