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Chapter 1: Problem 25
Evaluate the following expressions or state that the quantity is undefined. Use a calculator only to check your work. $$\cos (-\pi)$$
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Modify Exercise 84 and use property \(\mathrm{E} 2\) for exponents to prove that \(\log _{b}(x / y)=\log _{b} x-\log _{b} y\).
Prove the following identities. $$\sin ^{-1} y+\sin ^{-1}(-y)=0$$
Verify that the function $$ D(t)=2.8 \sin \left(\frac{2 \pi}{365}(t-81)\right)+12 $$ has the following properties, where \(t\) is measured in days and \(D\) is measured in hours. a. It has a period of 365 days. b. Its maximum and minimum values are 14.8 and \(9.2,\) respectively, which occur approximately at \(t=172\) and \(t=355\) respectively (corresponding to the solstices). c. \(\overline{D(81)}=12\) and \(D(264)=12\) (corresponding to the equinoxes).
Make a sketch of the given pairs of functions. Be sure to draw the graphs accurately relative to each other. $$y=x^{1 / 3} \text { and } y=x^{1 / 5}$$
Determine a polynomial \(f\) that satisfies the following properties. $$(f(x))^{2}=x^{4}-12 x^{2}+36$$
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