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Chapter 4: Problem 31
Evaluate the trigonometric function using its period as an aid. $$\sin 4 \pi$$
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Complete the equation.
$$\arccos \frac{x-2}{2}=\arctan (\text{_____}), \quad 2
Consider the function \(f(x)=x-\cos x\) (a) Use a graphing utility to graph the function and verify that there exists a zero between 0 and \(1 .\) Use the graph to approximate the zero. (b) Starting with \(x_{0}=1,\) generate a sequence \(x_{1}, x_{2}\) \(x_{3}, \ldots,\) where \(x_{n}=\cos \left(x_{n-1}\right) .\) For example \(x_{0}=1\) \(x_{1}=\cos \left(x_{0}\right)\) \(x_{2}=\cos \left(x_{1}\right)\) \(x_{3}=\cos \left(x_{2}\right)\) What value does the sequence approach?
\(A\) fan motor turns at a given angular speed. How does the speed of the tips of the blades change when a fan of greater diameter is on the motor? Explain.
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 \(f(x) \rightarrow\) $$f(x)=\csc x$$
Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\sin x+\cos \left(x+\frac{\pi}{2}\right), \quad g(x)=0$$
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