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Chapter 5: Problem 6
Verify each identity. $$\cot x \sec x \sin x=1$$
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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.
Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$2 \tan ^{2} x+5 \tan x+3=0$$
Find the inverse of \(f(x)=\frac{x-1}{x+1}\) (Section \(1.8, \text { Example } 4)\)
In the interval \([0,2 \pi),\) the solutions of \(\sin x=\cos 2 x\) are \(\frac{\pi}{6}, \frac{5 \pi}{6},\) and \(\frac{3 \pi}{2} .\) Explain how to use graphs generated by a graphing utility to check these solutions.
Will help you prepare for the material covered in the next section.$$\text { Give exact values for } \sin 30^{\circ}, \cos 30^{\circ}, \sin 60^{\circ}, \text { and } \cos 60^{\circ}$$
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