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Chapter 5: Problem 68
Use the cofunction identities to evaluate the expression without using a calculator. $$\tan ^{2} 63^{\circ}+\cot ^{2} 16^{\circ}-\sec ^{2} 74^{\circ}-\csc ^{2} 27^{\circ}$$
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Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the given interval. $$3 \tan ^{2} x+5 \tan x-4=0, \quad\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$
Find the \(x\) -intercepts of the graph. $$y=\sec ^{4}\left(\frac{\pi x}{8}\right)-4$$
The displacement from equilibrium of a weight oscillating on the end of a spring is given by \(y=1.56 e^{-0.22 t} \cos 4.9 t,\) where \(y\) is the displacement (in feet) and \(t\) is the time (in seconds). Use a graphing utility to graph the displacement function for \(0 \leq t \leq 10\). Find the time beyond which the displacement does not exceed 1 foot from equilibrium.
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\sec ^{2} x+0.5 \tan x-1=0$$
Determine whether the statement is true or false. Justify your answer. The equation \(2 \sin 4 t-1=0\) has four times the number of solutions in the interval \([0,2 \pi)\) as the equation \(2 \sin t-1=0\).
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