Graphing Sin, Cos, Sec & Csc

A cosecant function has a period of

 $4\pi$  . Which of the following could be this function?

•  $y=\csc\left(4\pi x\right)$  

•  $y=\csc\left(4x\right)$  

•  $y=\csc\left(\frac{1}{4}x\right)$  

•  $y=\csc\left(\frac{1}{2}x\right)$  

The __________ represents the distance from the baseline of sine/cosine to the max and min of the curve.

• Period

• Frequency

• Max/Min

• Amplitude

What is the range of $y=3\sin2x$  ?

•  $\left[-2,\ 2\right]$  

•  $\left(-2,\ 2\right)$  

•  $\left(-3,\ 3\right)$ 

•  $\left[-3,\ 3\right]$  

Which equation meets the following requirements?
Domain:  $\left(-\infty,\ \infty\right)$  

Range:   $\left[-2,\ 2\right]$  

•  $y=-2\sin\frac{1}{3}x$  
  

•  $y=\cos2x$  
  

•  $y=2\csc3x$  
  

•  $y=\frac{1}{2}\sec2x$  
  

Which equation meets the following requirements?
Domain:  $x\ne\frac{3\pi}{2},\ \frac{9\pi}{4},...$  

Range:   $\left(-\infty,\ -4\right]\cup\left[4,\ \infty\right)$  

•  $y=-4\sin\frac{1}{3}x$  
  

•  $y=\frac{1}{3}\cos2x$  
  

•  $y=\frac{1}{3}\csc4x$  
  

•  $y=4\sec\frac{1}{3}x$  
  

Where do the vertical asymptotes fall for the function $y=-\frac{2}{3}\sec5x$  ?

•  $0,\ \frac{\pi}{5},\ \frac{2\pi}{5}$  

•  $\frac{3\pi}{4},\ \frac{9\pi}{4}$  

•  $\frac{\pi}{10},\ \frac{3\pi}{10}$  

•  $0,\ \frac{3\pi}{2},\ \frac{\pi}{10},\ 3\pi$  

Which function has the same period as $y=4\csc2x$  ?

•  $y=4\cos x$  

•  $y=-4\sin2x$  

•  $y=2\sec4x$  

•  $y=-2\csc4x$  

What is the amplitude of

 $y=-5\csc2x$  ?

• 5

• -5

•  $\frac{1}{4}$  

• None

What is the minimum value in the range of $y=2\sin\frac{1}{3}x$ ? 

• 2

•  $\frac{1}{3}$  

•  $6\pi$  

• -2