Determine the exact value of the given inverse trigonometric function without using a calculator. y = csc ⁡ − 1 ( − 2 3 3 ) y=\csc^{-1}\left(-\frac{2\sqrt3}{3}\right) y = csc − 1 ( − 3 2 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> )

y = − π 3 y=-\frac{\pi}{3} y = − 3 π

y = π 3 y=\frac{\pi}{3} y = 3 π

y = − π 6 y=-\frac{\pi}{6} y = − 6 π

y = π 6 y=\frac{\pi}{6} y = 6 π

Inverse Sine, Cosine, & Tangent

5. Inverse Trigonometric Functions and Basic Trigonometric Equations / Inverse Sine, Cosine, & Tangent / Problem 6

Problem 6

Determine the exact value of the given inverse trigonometric function without using a calculator.
$y=\csc^{-1}\left(-\frac{2\sqrt3}{3}\right)$

$y=\frac{\pi}{3}$

$y=-\frac{\pi}{3}$

$y=-\frac{\pi}{6}$

$y=\frac{\pi}{6}$