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Chapter 6: Problem 92
Use the sum-to-product formulas to find the exact value of the expression. $$\sin \frac{5 \pi}{4}-\sin \frac{3 \pi}{4}$$
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Sketch the graph of the function. (Include two full periods.) $$f(x)=\frac{1}{2} \cot \left(x+\frac{\pi}{4}\right)$$
Use the figure, which shows two lines whose equations are \(y_{1}=m_{1} x+b_{1}\) and \(y_{2}=m_{2} x+b_{2}\). Assume that both lines have positive slopes. Derive a formula for the angle between the two lines. Then use your formula to find the angle between the given pair of lines. $$\begin{aligned} &y=x\\\ &y=\frac{1}{\sqrt{3}} x \end{aligned}$$
(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment connecting the points. $$(5,2),(-1,4)$$
Find the \(x\) - and \(y\) -intercepts of the graph of the equation. Use a graphing utility to verify your results. $$y=-\frac{1}{2}(x-10)+14$$
Find the exact values of \(\sin (u / 2), \cos (u / 2),\) and \(\tan (u / 2)\)
using the half-angle formulas.
$$\sin u=\frac{5}{13}, \quad \pi / 2
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