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Chapter 4: Problem 43
Evaluate the trigonometric function of the quadrant angle. $$ \csc \pi $$
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Fill in the blanks. $$ \begin{array}{ll} \text { Function } & \text { Alternative Notation } & \text { Domain } & \text { Range } \end{array} $$ $$ y=\arcsin x \quad-\frac{\pi}{2} \leq y \leq \frac{\pi}{2} $$
Sketch the graph of the function. Include two full periods. $$ y=2 \cot \left(x+\frac{\pi}{2}\right) $$
Use a graphing utility to graph the function. Include two full periods. $$ y=\tan \left(x-\frac{\pi}{4}\right) $$
PATTERN RECOGNITION (a) Use a graphing utility to graph each function. $$ \begin{array}{l} y_{1}=\frac{4}{\pi}\left(\sin \pi x+\frac{1}{3} \sin 3 \pi x\right) \\ y_{2}=\frac{4}{\pi}\left(\sin \pi x+\frac{1}{3} \sin 3 \pi x+\frac{1}{5} \sin 5 \pi x\right) \end{array} $$ (b) Identify the pattern started in part (a) and find a function \(y_{3}\) that continues the pattern one more term. Use a graphing utility to graph \(y_{3}\) (c) The graphs in parts (a) and (b) approximate the periodic function in the figure. Find a function \(y_{4}\) that is a better approximation.
Evaluate the expression without using a calculator. $$ \sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right) $$
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