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Chapter 5: Problem 21
Find the exact value of each expression. $$\tan \left(\frac{\pi}{6}+\frac{\pi}{4}\right)$$
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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. $$\sin 60^{\circ} \sin 30^{\circ}=\frac{1}{2}\left[\cos \left(60^{\circ}-30^{\circ}\right)-\cos \left(60^{\circ}+30^{\circ}\right)\right]$$
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 below its rest position.
Use the appropriate values from Exercise 110 to answer each of the following. a. Is \(\cos \left(2 \cdot 30^{\circ}\right),\) or \(\cos 60^{\circ},\) equal to \(2 \cos 30^{\circ} ?\) b. Is \(\cos \left(2 \cdot 30^{\circ}\right),\) or \(\cos 60^{\circ},\) equal to \(\cos ^{2} 30^{\circ}-\sin ^{2} 30^{\circ} ?\)
Solve each equation on the interval \([0,2 \pi)\) Do not use a calculator. $$\sin x+2 \sin \frac{x}{2}=\cos \frac{x}{2}+1$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. The word identity is used in different ways in additive identity, multiplicative identity, and trigonometric identity.
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