Question

Help me. How do I find the exact value of negative radians?!?!??!

Answer 1

\[\csc -4\pi/3\]

Answer 2

you know how to find \(-\frac{4\pi}{3}\)on the unit circle?

Answer 3

no where would negative 4pi/3 be?

Answer 4

Is easier if you solve it like this.
\[\csc(x)=1/sen(x)\]
if Pi=180º to find out what angle you will forma you need to multiply it by -4/3;
-4/3pi= -240º
A negative angle means you have extract it from the angle 0º, follow a contrary path you are used with a circle.

Here you notice -240º=120º , the negative sign only means you are going on the contray direction common angles are measured.
\[\csc(-240º)=\csc(120º)=1/sen(120º)=\csc(-4\pi/3)\]
\[\csc(-4\pi/3)=1/sen(120º)\]