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Chapter 4: Problem 44
Sketch the graph of the function. (Include two full periods.) $$y=\sin 4 x$$
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Prove each identity. (a) \(\arcsin (-x)=-\arcsin x\) (b) \(\arctan (-x)=-\arctan x\) (c) \(\arctan x+\arctan \frac{1}{x}=\frac{\pi}{2}, \quad x>0\) (d) \(\arcsin x+\arccos x=\frac{\pi}{2}\) (e) \(\arcsin x=\arctan \frac{x}{\sqrt{1-x^{2}}}\)
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? $$f(t)=3 \cos 2 t+3 \sin 2 t$$
Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin \frac{x}{2}$$
Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin (x-1)$$
Determine whether the statement is true or false. Justify your answer. You can obtain the graph of \(y=\sec x\) on a calculator by graphing a translation of the reciprocal of \(y=\sin x\)
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