use a calculator to find the value of the expression.\n\n\\( \\csc ^ { - 1 } \\left( - \\frac { 4 } { 3 }…

use a calculator to find the value of the expression.\n\n\\( \\csc ^ { - 1 } \\left( - \\frac { 4 } { 3 } \\right) \\)\n\n\\( \\csc ^ { - 1 } \\left( - \\frac { 4 } { 3 } \\right) \\approx \\square \\)\n(type your answer in radians. round to two decimal places as needed.)

use a calculator to find the value of the expression.\n\n\\( \\csc ^ { - 1 } \\left( - \\frac { 4 } { 3 } \\right) \\)\n\n\\( \\csc ^ { - 1 } \\left( - \\frac { 4 } { 3 } \\right) \\approx \\square \\)\n(type your answer in radians. round to two decimal places as needed.)

Answer

Explanation:

Step1: Use the identity $\csc^{-1}x=\sin^{-1}\frac{1}{x}$

$$\csc^{-1}\left(-\frac{4}{3}\right)=\sin^{-1}\left(-\frac{3}{4}\right)$$

Step2: Calculate $\sin^{-1}\left(-\frac{3}{4}\right)$ using a calculator

Set the calculator to radian mode. Then input $\sin^{-1}\left(-\frac{3}{4}\right)$.

Answer:

$-0.85$