Question

use the unit circle csc(3/2)

Answer 1

Using the unit circle, we can see that 3π/2 is equal to 270º

Then we can say that

$\begin{gathered} \cos \frac{3\pi}{2}=0 \\ \\ \sin \frac{3\pi}{2}=-1 \end{gathered}$

But the csc(x) is

$\csc (x)=\frac{1}{\sin (x)}$

Therefore

$\csc \frac{3\pi}{2}=\frac{1}{\sin \frac{3\pi}{2}}$

As we saw, sin(3π/2) = -1, then

$\csc \frac{3\pi}{2}=\frac{1}{-1}=-1$

Hence, the final answer is:

$\csc \mleft(\frac{3\pi}{2}\mright)=-1$