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Chapter 4: Problem 44
Use an inverse trigonometric function to write \(\theta\) as a function of \(x .\)
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Fill in the blank. If not possible, state the reason. As \(x \rightarrow \infty,\) the value of arctan \(x \rightarrow\) ___.
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. \(f(x)=\sin (\arctan 2 x), \quad g(x)=\frac{2 x}{\sqrt{1+4 x^{2}}}\)
Write the function in terms of the sine function by using the identity \(A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).\) Use a graphing utility to graph both forms of the function. What does the graph imply? \(f(t)=3 \cos 2 t+3 \sin 2 t\)
Evaluate the expression without using a calculator. \(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\)
Find the exact value of the expression. (Hint: Sketch a right triangle.) \(\sec \left[\arctan \left(-\frac{3}{5}\right)\right]\)
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