Chapter 5: Problem 77
Describe how you feel when you successfully verify a difficult identity. What other activities do you engage in that evoke the same feelings?
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Chapter 5: Problem 77
Describe how you feel when you successfully verify a difficult identity. What other activities do you engage in that evoke the same feelings?
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Solve and graph the solution set on a number line: $$\frac{2 x-3}{8} \leq \frac{3 x}{8}+\frac{1}{4}$$ (Section P.9, Example 5 )
Use this information to solve. A ball on a spring is pulled 4 inches below its rest position and then released. After t seconds, the balls distance, \(d\), in inches from its rest position is given by $$d=-4 \cos \frac{\pi}{3} t$$ Find all values of \(t\) for which the ball is 2 inches above its rest position.
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. $$\sin \pi \cos \frac{\pi}{2}=\frac{1}{2}\left[\sin \left(\pi+\frac{\pi}{2}\right)+\sin \left(\pi-\frac{\pi}{2}\right)\right]$$
Remembering the six sum and difference identities can be difficult. Did you have problems with some exercises because the identity you were using in your head turned out to be an incorrect formula? Are there easy ways to remember the six new identities presented in this section? Group members should address this question, considering one identity at a time. For each formula, list ways to make it casier to remember.
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 \(2 \sin 30^{\circ} \cos 30^{\circ} ?\)
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