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Chapter 6: Problem 81
Use words to describe the formula for each of the following: the cosine of the difference of two angles.
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Solve each equation on the interval \([0,2 \pi)\) Do not use a calculator. $$ 2 \cos x-1+3 \sec x=0 $$
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. $$ \cos ^{2} x+2 \cos x-2=0 $$
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. $$ 7 \cos x=4-2 \sin ^{2} x $$
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.
Exercises \(110-112\) will help you prepare for the material covered in the next section. Use the appropriate values from Exercise 110 to answer each of the following. a. Is \(\cos \left(2 \cdot 30^{\circ}\right),\) or \(\cos 60^{\circ},\) equal to \(2 \cos 30^{\circ} ?\) b. Is \(\cos \left(2 \cdot 30^{\circ}\right),\) or \(\cos 60^{\circ},\) equal to \(\cos ^{2} 30^{\circ}-\sin ^{2} 30^{\circ} ?\)
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