Graphing Trig Functions

Where does the graph of y=sin(x) begin its first cycle?

• (0,1)

• (0,0)

• (1,0)

• $\left(0,\pi\right)$

Where does the graph of y=cos(x) begin its first cycle?

• (0,1)

• (0,0)

• (1,0)

• $\left(0,\pi\right)$

What is the period of the following graphs?

• $\pi$

• $2\pi$

• 4

• $\frac{\pi}{2}$

What is the period of both the parent graphs for tangent and cotangent?

•  $2\pi$  

•  $\frac{\pi}{4}$  

•  $\pi$  

•  $\frac{\pi}{2}$  

What is the period of the graph

 $y=2\csc\left(2x\right)+1$  

• 2

•  $2\pi$  

•  $4\pi$  

•  $\pi$  

What is the amplitude of

y = -3sec (7x) -2

• 3

• -3

• -2

• 7

What is the horizontal shift of

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

•  $Left\ \frac{\pi}{2}$  

•  $Right\ \frac{\pi}{4}$  

•  $Right\ \frac{\pi}{2}$  

•  $Left\ \frac{\pi}{4}$  

Check all of the following that are true for the graph

y=4 cot (-3x) -2

• Amplitude = 2

• Amplitude = 4

• x-axis flip

• y-axis flip

• Vertical Shift: Up 2

What is the range of

y=2csc(x) -1

• $\left(-\infty,-2\right]U\left[2,\infty\right)$

• All Real Numbers

• $\left(-\infty,-2\right]U\ \left[0,\infty\right)$

• $\left(-\infty,-3\right]U\left[1,\infty\right)$

Where are the asymptotes of

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

•  $x=\pi n$  

•  $x=\frac{\pi}{2}+\pi n$  

•  $x=\frac{\pi}{4}+\pi n$  

• There are no asymptotes