12 Graphs & Properties of tan, cot, sec, csc

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

$y=2\cot\left(2x\right)$

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

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

all real numbers except odd multiples of  $\frac{\pi}{4}$  

all real numbers except multiples of $\frac{\pi}{2}$ 

all real numbers except multiples of $\pi$ 

all real numbers

all real numbers

all real numbers except odd multiples of  $\frac{\pi}{2}$  

$y=\cot\left(2x\right)$

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

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

$y=\tan\left(x\right)$

all real numbers except odd multiples of $\frac{\pi}{2}$

all real numbers except multiples of $\frac{\pi}{2}$

all real numbers except multiples of $\pi$

all real numbers

all real numbers

all real numbers except odd multiples of $\frac{\pi}{2}$

all multiples of  $\frac{\pi}{4}$  

odd multiples of  $\frac{\pi}{4}$  

odd multiples of  $\frac{\pi}{2}$  

all multiples of  $\frac{\pi}{2}$  

all multiples of $\frac{\pi}{4}$

odd multiples of $\frac{\pi}{4}$

odd multiples of $\frac{\pi}{2}$

all multiples of $\frac{\pi}{2}$

$y=3\csc\left(2x\right)$

$y=2\csc\left(3x\right)$

$y=2\sec\left(3x\right)$

$y=3\sec\left(\pi x\right)$

all real numbers

all real numbers except odd multiples of $\frac{\pi}{2}$