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Chapter 6: Problem 86
Use words to describe the formula for each of the following: the tangent of the sum of two angles.
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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.
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. $$ \tan (\pi-x)=-\tan x $$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. After using an identity to determine the exact value of \(\sin 105^{\circ},\) I verified the result with a calculator.
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. $$ \cos ^{2} x+2 \cos x-2=0 $$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(4 \cos ^{2} x=5-4 \sin x\) by working independently with the left side, applying a Pythagorean identity, and transforming the left side into \(5-4 \sin x .\)
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