Graphing Sine and Cosine

What is the amplitude of the following function?

 $y=-4\sin2\left(x+\frac{\pi}{2}\right)-5$  

•  $-4$  

•  $4$  

•  $2\pi$  

•  $\pi$  

•  $-5$  

Tags

CCSS.HSF.TF.B.5

What is the period of the following function?

 $y=-4\sin2\left(x+\frac{\pi}{2}\right)-5$  

•  $-4$  

•  $4$  

•  $2\pi$  

•  $\pi$  

•  $-5$  

Tags

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.5

What is the midline of the following function?

 $y=-4\sin2\left(x+\frac{\pi}{2}\right)-5$  

•  $-4$  

•  $4$  

•  $2\pi$  

•  $\pi$  

•  $-5$  

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.TF.B.5

What are the transformations of g(x)? Select all the apply. $g\left(x\right)=-4\sin2\left(x+\frac{\pi}{2}\right)-5$  

• reflected over the x-axis

• vertical stretch by a factor of 4

• horizontal shrink by a factor of  $\frac{1}{2}$  

• left  $\frac{\pi}{2}$  

• down 5

Tags

CCSS.HSF.BF.B.3

What is the midline of the following function? $y=\frac{1}{2}\cos\left(x-\frac{\pi}{4}\right)+2$  

•  $\frac{1}{2}$  

•  $2\pi$  

•  $\pi$  

•  $2$  

•  $\frac{\pi}{4}$  

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.TF.B.5

What is the amplitude of the following function? $y=\frac{1}{2}\cos\left(x-\frac{\pi}{4}\right)+2$  

•  $\frac{1}{2}$  

•  $2\pi$  

•  $\pi$  

•  $2$  

•  $\frac{\pi}{4}$  

Tags

CCSS.HSF.TF.B.5

What is the period of the following function? $y=\frac{1}{2}\cos\left(x-\frac{\pi}{4}\right)+2$  

•  $\frac{1}{2}$  

•  $2\pi$  

•  $\pi$  

•  $2$  

•  $\frac{\pi}{4}$  

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.4

What are the transformations of  $g\left(x\right)$  ? Select all that apply.
 $g\left(x\right)=\frac{1}{2}\cos\left(x-\frac{\pi}{4}\right)+2$  

• vertical stretch by a factor of  $2$  

• vertical shrink by a factor of  $\frac{1}{2}$  

• right  $\frac{\pi}{4}$  

• left  $\frac{\pi}{4}$  

• up  $2$  

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Write an equation in the form $y=a\cos bx$  so that the graph has the an amplitude of  $10$  and a period of  $4$  .

•  $y=10\ \sin\ \frac{\pi}{2}x$  

•  $y=4\ \cos\ \frac{\pi}{5}x$  

•  $y=10\ \cos\ \frac{\pi}{2}x$  

•  $y=10\ \cos\ 2\pi x$  

•  $y=2\ \sin\ \frac{\pi}{5}x$  

Tags

CCSS.HSF.TF.B.5

Write an equation in the form $y=a\ \sin bx$  so that the graph has the an amplitude of  $2$  and a period of  $2\pi$  .

•  $y=2\sin x$  

•  $y=2\cos x$  

•  $y=2\cos2\pi x$  

•  $y=2\pi\ \sin2x$  

•  $y=2\pi\sin2x$  

Tags

CCSS.HSF.TF.B.5