4.5 Graph Sine & Cosine

The period of a sine or cosine graph can be found by ....

• It's always $2\pi$

• $\frac{2\pi}{b}$

• $b\cdot\left(2\pi\right)$

• $2\pi+b$

What is the domain and range of  $y=\sin\ x$  and  $y=\cos x$  ?

• D: (-∞, ∞)

  R: [-1, 1]

• D: (-∞, ∞)

  R: [-π, π]

• D: (∞, -∞)

  R: [-1, 1]

• D: (-∞, ∞)

  R: [-∞, ∞]

Find the amplitude of  $y=-4\cos\left(\frac{1}{4}x+\frac{\pi}{4}\right)-4$ 

• 4

• -4

• 1

• -1

Find the period of $y=2\sin\left(\frac{1}{4}x-\frac{\pi}{2}\right)$  

•  $\frac{\pi}{2}$  

•  $8\pi$  

•  $4\pi$  

•  $\pi$  

Tags

CCSS.HSF-IF.C.7E

Find the phase shift of  $y=-4\cos\left(\frac{1}{4}x+\frac{\pi}{4}\right)$  

• 2π units to the right

• π units to the right

• π units to the left

• 2π units to the left

Tags

CCSS.HSF-IF.C.7E

Check each characteristic that is TRUE for the equation $y=2\sin\left(6x-\frac{\pi}{4}\right)-2$  

• Amplitude is 2

• Amplitude is -2

• Midline is y=2

• Midline is y=-2

• Phase shift is π/24 to the right

Tags

CCSS.HSF-IF.C.7E

Write an equation of a reflected sine function with a period of  $\frac{4\pi}{3}$  and amplitude of 7 that has been phase shifted  $4\pi$  units to the left and has a midline at  $y=-2$  

•  $y=-7\sin\left(\frac{3}{2}x+6\pi\right)-2$  

•  $y=7\sin\left(\frac{4\pi}{3}x-\frac{16\pi}{3}\right)+2$  

•  $y=-7\sin\left(\frac{3}{2}x+4\pi\right)+2$  

•  $y=\frac{3}{2}\sin\left(7x-4\pi\right)-2$  

Write the equation for a cosine function with an amplitude of 1/2, period of π/4 that has been shifted right π/3.

• 
  

  $y=\frac{1}{2}\cos\left(8x-\frac{8\pi}{3}\right)$
  

• $y=8\cos\left(\frac{\pi}{4}x-\frac{\pi}{8}\right)$

• $y=2\cos\left(\frac{x}{8}+\frac{\pi}{24}\right)$

• $y=\frac{1}{2}\cos8x-\frac{\pi}{3}$

What is one possible equation of the graph?

• 
  

  $y=-2\cos\left(x-\frac{3\pi}{2}\right)$

• $y=-\sin x+1$

• $y=2\sin\left(x-\frac{\pi}{2}\right)$

• $y=\cos2x$

Tags

CCSS.HSF-IF.C.7E

What is one possible equation of this graph?

• y=cos2x

• y=2sin2x

• y=2cos2x

• y=2sinx

Tags

CCSS.HSF-IF.C.7E