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Chapter 5: Problem 1
Verify each identity. $$\sin x \sec x=\tan x$$
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Use this information to solve. Our cycle of normal breathing takes place every 5 seconds. Velocity of air flow, \(y,\) measured in liters per second, after \(x\) seconds is modeled by $$y=0.6 \sin \frac{2 \pi}{5} x$$ Velocity of air flow is positive when we inhale and negative when we exhale. Within each breathing cycle, when are we inhaling at a rate of 0.3 liter per second? Round to the nearest tenth of a second.
Solve each equation on the interval \([0,2 \pi)\) Do not use a calculator. $$2 \cos x-1+3 \sec x=0$$
Use the power-reducing formulas to rewrite \(\sin ^{6} x\) as an equivalent expression that does not contain powers of trigonometric functions greater than 1
Will help you prepare for the material covered in the next section. $$\text { Solve: } 2\left(1-u^{2}\right)+3 u=0$$
Graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, this indicates that the equation is not an identity. In these exercises, find a value of \(x\) for which both sides are defined but not equal. $$\cos 1.2 x \cos 0.8 x-\sin 1.2 x \sin 0.8 x=\cos 2 x$$
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