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

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 reciprocal identity

We know that (\csc^{-1}x=\sin^{-1}\left(\frac{1}{x}\right)) for (|x|\geq1). So, (\csc^{-1}\left(-\frac{4}{3}\right)=\sin^{-1}\left(-\frac{3}{4}\right))

Step2: Use a calculator

Set the calculator to radian mode. Then, calculate (\sin^{-1}\left(-\frac{3}{4}\right)). Using a calculator, (\sin^{-1}\left(-\frac{3}{4}\right)\approx - 0.85) (rounded to two decimal places)

Answer:

(-0.85)