91Ó°ÊÓ

In Exercises 75-78, find the smallest positive value of \(x\) that makes the statement true. Give the answer in degrees and round to two decimal places. $$ e^{x}-\tan x=0 $$

For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to solve the equation \(\sin \theta=\cos (2 \theta)\) on \(0 \leq \theta<\pi\).

For Exercises 87-92, refer to the following: Graphing calculators can be used to find approximate solutions to trigonometric equations. For the equation \(f(x)=g(x)\), let \(Y_{1}=f(x)\) and \(Y_{2}=g(x)\). The \(x\) values that correspond to points of intersections represent solutions. Use a graphing utility to find all solutions to the equation \(\cos \theta=e^{\theta}\) for \(\theta \geq 0\).

In Exercises 117-120, determine whether each statement is true or false. $$ \text { The inverse cosecant function is an odd function. } $$

In Exercises 117-120, determine whether each statement is true or false. $$ \text { Explain why } \sec ^{-1}\left(\frac{1}{2}\right) \text { does not exist. } $$