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Chapter 4: Problem 20
Evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=\frac{5 \pi}{3}$$
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The numbers of hours \(H\) of daylight in Denver, Colorado, on the 15 th of each month are: \(1(9.67), 2(10.72), \quad 3(11.92), \quad 4(13.25)\) \(5(14.37), \quad 6(14.97), \quad 7(14.72), \quad 8(13.77), \quad 9(12.48)\) \(10(11.18), \quad 11(10.00), \quad 12(9.38) . \quad\) The month is represented by \(t,\) with \(t=1\) corresponding to January. A model for the data is \(H(t)=12.13+2.77 \sin \left(\frac{\pi t}{6}-1.60\right)\) (a) Use a graphing utility to graph the data points and the model in the same viewing window. (b) What is the period of the model? Is it what you expected? Explain. (c) What is the amplitude of the model? What does it represent in the context of the problem? Explain.
Use a graphing utility to graph the function. $$f(x)=2 \arccos (2 x)$$
Determine whether the statement is true or false. Justify your answer. $$\arctan x=\frac{\arcsin x}{\arccos x}$$
Finding Arc Length Find the length of the are on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). $$r=15 \text { inches, } \theta=120^{\circ}$$
Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) As \(x \rightarrow 0^{+},\) the value of \(f(x) \rightarrow\) (b) As \(x \rightarrow 0^{-},\) the value of \(f(x) \rightarrow\) (c) As \(x \rightarrow \pi^{+},\) the value of \(f(x) \rightarrow\) (d) As \(x \rightarrow \pi^{-},\) the value of \(f(x) \rightarrow\) $$f(x)=\csc x$$
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