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Chapter 1: Problem 11
\(t=\frac{3 \pi}{2}\)
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In Exercises 69 and 70, use a graphing utility to graph \(f\) and \(g\) in the same viewing window to verify that the two functions are equal. Explain why they are equal. Identify any asymptotes of the graphs. $$ f(x)=\sin (\arctan 2 x), \quad g(x)=\frac{2 x}{\sqrt{1+4 x^{2}}} $$
In Exercises 59-68, write an algebraic expression that is equivalent to the expression. (Hint: Sketch a right triangle, as demonstrated in Example 7.) $$ \cos (\arcsin 2 x) $$
$$ \text { In Exercises 49-58, find the exact value of the expression. } $$ $$ \tan \left[\arcsin \left(-\frac{3}{4}\right)\right] $$
In Exercises 109-112, sketch a right triangle corresponding to the trigonometric function of the acute angle \(\theta\). Use the Pythagorean Theorem to determine the third side. Then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$ \sec \theta=3 $$
In Exercises 19-34, use a calculator to evaluate the expression. Round your result to two decimal places. $$ \arcsin (-0.125) $$
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