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Chapter 4: Problem 4
The number of cycles per second of a point in simple harmonic motion is its _____.
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Evaluate the expression without using a calculator. \(\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)\)
Fill in the blank. If not possible, state the reason. As \(x \rightarrow 1^{-},\) the value of \(\arccos x \rightarrow\) ___.
Evaluate the expression without using a calculator. \(\arccos 0\)
Fill in the blank. If not possible, state the reason. As \(x \rightarrow-\infty,\) the value of arctan \(x \rightarrow\) ___.
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) \(\arcsin x=\arctan \frac{x}{\sqrt{1-x^{2}}}\)
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