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Chapter 4: Problem 38
Evaluate the trigonometric function of the quadrant angle, if possible. $$\csc \frac{3 \pi}{2}$$
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Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(240.6^{\circ}\) (b) \(-145.8^{\circ}\)
For the simple harmonic motion described by the trigonometric function, find (a) the maximum displacement, (b) the frequency, (c) the value of \(d\) when \(t=5,\) and (d) the least positive value of \(t\) for which \(d=0 .\) Use a graphing utility to verify your results. $$d=\frac{1}{64} \sin 792 \pi t$$
Finding Arc Length Find the length of the are on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). $$r=15 \text { inches, } \theta=120^{\circ}$$
Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi),\) and sketch the graph of the inverse trigonometric function.
Determine whether the statement is true or false. Justify your answer. $$\arctan x=\frac{\arcsin x}{\arccos x}$$
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