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Chapter 6: Problem 15
Verify the identity. $$\cos ^{2} \beta-\sin ^{2} \beta=1-2 \sin ^{2} \beta$$
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(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment connecting the points. $$(5,2),(-1,4)$$
Fill in the blanks. (Note: \(x \rightarrow c^{+}\) indicates that \(x\) approaches \(c\) from the right, and \(x \rightarrow c^{-}\) indicates that \(x\) approaches \(c\) from the left.) $$\text { As } x \rightarrow \pi^{-}, \sin x \rightarrow$$ _______ $$\text { and csc } x \rightarrow$$ _______.
Use the sum-to-product formulas to write the sum or difference as a product. $$\cos \left(\theta+\frac{\pi}{2}\right)-\cos \left(\theta-\frac{\pi}{2}\right)$$
Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. $$67^{\circ} 30^{\prime}$$
Find the exact values of \(\sin (u / 2), \cos (u / 2),\) and \(\tan (u / 2)\)
using the half-angle formulas.
$$\sec u=\frac{7}{2}, \quad 0
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