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Chapter 5: Problem 15
Determine the amplitude and period of each function. Then graph one period of the function. $$y=-\sin \frac{2}{3} x$$
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Graph each pair of functions in the same viewing rectangle. Use your knowledge of the domain and range for the inverse trigonometric function to select an appropriate viewing rectangle. How is the graph of the second equation in cach exercise related to the graph of the first equation? $$ y=\sin ^{-1} x \text { and } y=\sin ^{-1} x+2 $$
We will prove the following identities: $$\begin{array}{l} {\sin ^{2} x=\frac{1}{2}-\frac{1}{2} \cos 2 x} \\ {\cos ^{2} x=\frac{1}{2}+\frac{1}{2} \cos 2 x} \end{array}$$ Use the identity for \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)
This exercise is intended to provide some fun with biorhythms, regardless of whether you believe they have any validity. We will use each member鈥檚 chart to determine biorhythmic compatibility. Before meeting, each group member should go online and obtain his or her biorhythm chart. The date of the group meeting is the date on which your chart should begin. Include 12 months in the plot. At the meeting, compare differences and similarities among the intellectual sinusoidal curves. Using these comparisons, each person should find the one other person with whom he or she would be most intellectually compatible.
Write as a single logarithm: \(\frac{1}{2} \log x+6 \log (x-2)\) (Section \(4.3, \text { Example } 6)\)
Use a sketch to find the exact value of each expression. $$ \sec \left[\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)\right] $$
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