삼각함수를 포함한 방정식과 부등식

For the following exercises, find the function if $\sin \,t=\frac{x}{x+1}.$

$\cos \,t$

For the following exercises, find the function if $\sin \,t=\frac{x}{x+1}.$

$\sec \,t$

For the following exercises, find the function if $\sin \,t=\frac{x}{x+1}.$

$\cot \,t$

For the following exercises, find the function if $\sin \,t=\frac{x}{x+1}.$

$\cos \left({\sin }^{-1}\left(\frac{x}{x+1}\right)\right)$

For the following exercises, find the function if $\sin \,t=\frac{x}{x+1}.$

${\tan }^{-1}\left(\frac{x}{\sqrt{2x+1}}\right)$

For what value of $x$ does $\sin \,x={\sin }^{-1}x?$ Use a graphing calculator to approximate the answer.

For what value of $x$ does $\cos \,x={\cos }^{-1}x?$ Use a graphing calculator to approximate the answer.

An isosceles triangle has two congruent sides of length 9 inches. The remaining side has a length of 8 inches. Find the angle that a side of 9 inches makes with the 8-inch side.

Without using a calculator, approximate the value of $\arctan (10,000).$ Explain why your answer is reasonable.

The line $y=\frac{3}{5}x$ passes through the origin in the x,y-plane. What is the measure of the angle that the line makes with the positive x-axis?

The line $y=\frac{-3}{7}x$ passes through the origin in the x,y-plane. What is the measure of the angle that the line makes with the negative x-axis?

For the following exercises, find the exact value without the aid of a calculator.

${\sin }^{-1}(1)$

For the following exercises, find the exact value without the aid of a calculator.

${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

For the following exercises, find the exact value without the aid of a calculator.

${\tan }^{-1}(-1)$

For the following exercises, find the exact value without the aid of a calculator.

${\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)$

For the following exercises, find the exact value without the aid of a calculator.

${\sin }^{-1}\left(\frac{-\sqrt{3}}{2}\right)$

For the following exercises, find the exact value without the aid of a calculator.

${\sin }^{-1}\left(\cos \left(\frac{\pi }{6}\right)\right)$

For the following exercises, find the exact value without the aid of a calculator.

${\cos }^{-1}\left(\tan \left(\frac{3\pi }{4}\right)\right)$

For the following exercises, find the exact value without the aid of a calculator.

$\sin \left({\sec }^{-1}\left(\frac{3}{5}\right)\right)$

For the following exercises, find the exact value without the aid of a calculator.

$\cot \left({\sin }^{-1}\left(\frac{3}{5}\right)\right)$