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 (3\pi)/(2)=0 \\ \\ \sin (3\pi)/(2)=-1 \end{gathered}`

But the csc(x) is

`\csc (x)=(1)/(\sin (x))`

Therefore

`\csc (3\pi)/(2)=(1)/(\sin (3\pi)/(2))`

As we saw, sin(3π/2) = -1, then

`\csc (3\pi)/(2)=(1)/(-1)=-1`

Hence, the final answer is:

`\csc \mleft((3\pi)/(2)\mright)=-1`