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Chapter 5: Problem 75
Use the half-angle formulas to simplify the expression. $$-\sqrt{\frac{1-\cos 8 x}{1+\cos 8 x}}$$
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Write the expression as the sine, cosine, or tangent of an angle. $$\frac{\tan 140^{\circ}-\tan 60^{\circ}}{1+\tan 140^{\circ} \tan 60^{\circ}}$$
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x}=4$$
A Ferris wheel is built such that the height \(h\) (in feet) above ground of a seat on the wheel at time \(t\) (in minutes) can be modeled by \(h(t)=53+50 \sin \left(\frac{\pi}{16} t-\frac{\pi}{2}\right)\) The wheel makes one revolution every 32 seconds. The ride begins when \(t=0\). (a) During the first 32 seconds of the ride, when will a person on the Ferris wheel be 53 feet above ground? (b) When will a person be at the top of the Ferris wheel for the first time during the ride? If the ride lasts 160 seconds, how many times will a person be at the top of the ride, and at what times?
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\csc ^{2} x+0.5 \cot x-5=0$$
Write the expression as the sine, cosine, or tangent of an angle. $$\frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}}$$
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