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Chapter 5: Problem 39
Verify each identity. $$\sin (\alpha+\beta)+\sin (\alpha-\beta)=2 \sin \alpha \cos \beta$$
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Graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, this indicates the equation is not an identity. In these exercises, find a value of \(x\) for which both sides are defined but not equal. $$\cos \left(x+\frac{\pi}{4}\right)=\cos x+\cos \frac{\pi}{4}$$
Will help you prepare for the material covered in the next section.$$\text { Give exact values for } \sin 30^{\circ}, \cos 30^{\circ}, \sin 60^{\circ}, \text { and } \cos 60^{\circ}$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning.After using an identity to determine the exact value of \(\sin 105^{\circ}, 1\) verified the result with a calculator.
Determine the amplitude, period, and phase shift of \(y=4 \sin (2 \pi x+2) .\) Then graph one period of the function. (Section 4.5, Example 4 )
Group members are to write a helpful list of items for a pamphlet called "The Underground Guide to Verifying Identities." The pamphlet will be used primarily by students who sit, stare, and freak out every time they are asked to verify an identity. List easy ways to remember the fundamental identities. What helpful guidelines can you offer from the perspective of a student that you probably won't find in math books? If you have your own strategies that work particularly well, include them in the pamphlet.
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