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Chapter 5: Problem 57
Verify each identity. $$(\cos \theta-\sin \theta)^{2}+(\cos \theta+\sin \theta)^{2}=2$$
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Exercises \(116-118\) will help you prepare for the material covered in the next section. In each exercise, use exact values of trigonometric functions to show that the statement is true. Notice that each statement expresses the product of sines and/or cosines as a sum or a difference. $$\sin \pi \cos \frac{\pi}{2}=\frac{1}{2}\left[\sin \left(\pi+\frac{\pi}{2}\right)+\sin \left(\pi-\frac{\pi}{2}\right)\right]$$
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.
Use the appropriate values from Exercise 110 to answer each of the following. a. Is \(\sin \left(2 \cdot 30^{\circ}\right),\) or \(\sin 60^{\circ},\) equal to \(2 \sin 30^{\circ} ?\) b. Is \(\sin \left(2 \cdot 30^{\circ}\right),\) or \(\sin 60^{\circ},\) equal to \(2 \sin 30^{\circ} \cos 30^{\circ} ?\)
Determine the amplitude and period of \(y=3 \sin \frac{1}{2} x\) Then graph the function for \(0 \leq x \leq 4 \pi\) (Section 4.5, Example 3)
Will help you prepare for the material covered in the next section. $$\text { Solve: } 2\left(1-u^{2}\right)+3 u=0$$
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