Question

Find the exact value of the expression:
csc^-1 ((-2√3)/3) Explain please!

Answer 1

i think a good first step would be to recognize \(-\frac{2\sqrt{3}}{3}\) as \(-\frac{2}{\sqrt{3}}\)

Answer 2

and also recalling that \(\csc(x)\) is the reciprocal of \(\sin(x)\)

Answer 3

that way, you can ask "do i know an angle whose sine is \(-\frac{\sqrt{3}}{2}\) ?
if you do, you are done

Answer 4

Oy I didn't think of it that way, so it's π/3?

Answer 5

this is not tangent

Answer 6

actually it is \(-\frac{\pi}{3}\) because it is negative

Answer 7

Oh right! (:

Answer 8

picture works nice for problems like
\[\tan(\cos^{-1}(x))\] i.e.compositions

Answer 9

for these you just sort of have to know the answer

Answer 10

Thanks again c: