use a reference triangle to find the given angle.\n\\( \\sin ^ { - 1 } \\left( \\frac { \\sqrt { 3 } } { 2 }…

use a reference triangle to find the given angle.\n\\( \\sin ^ { - 1 } \\left( \\frac { \\sqrt { 3 } } { 2 } \\right) \\)\n\\( \\sin ^ { - 1 } \\left( \\frac { \\sqrt { 3 } } { 2 } \\right) = \\square \\)\n(type an exact answer in terms of \\( \\pi \\).)

use a reference triangle to find the given angle.\n\\( \\sin ^ { - 1 } \\left( \\frac { \\sqrt { 3 } } { 2 } \\right) \\)\n\\( \\sin ^ { - 1 } \\left( \\frac { \\sqrt { 3 } } { 2 } \\right) = \\square \\)\n(type an exact answer in terms of \\( \\pi \\).)

Answer

Explanation:

Step1: Recall the range of the inverse sine function

The range of (y = \sin^{-1}(x)) is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).

Step2: Recall the sine of special angles

We know that (\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}), and (\frac{\pi}{3}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right])

Answer:

(\frac{\pi}{3})