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Chapter 6: Problem 83

Use words to describe the formula for: the cosine of double an angle. (Describe one of the three formulas.)

Short Answer

Expert verified
The cosine of double an angle formula \( \cos(2A) \) can be described as the square of the cosine of the original angle subtracted by the square of the sine of the original angle, where \( A \) is the original angle.

Step by step solution

01

Understanding the Formula Symbols

The formula \( \cos(2A) = \cos^2(A) - \sin^2(A) \) has a few key symbols. The symbol \( \cos(2A) \) represents the cosine of an angle that is twice the size of angle A. The \( \cos^2(A) \) and \( \sin^2(A) \) symbols represent the square of the cosine and sine of angle A respectively.
02

Understanding the Formula Construction

The formula is structured such that the term \( \cos^2(A) - \sin^2(A) \) represents the value of \( \cos(2A) \) . Essentially, to find the cosine of a doubled angle, one can square the cosine of the angle and subtract the square of the sine of the angle.
03

Usage of the Formula

This formula is used when one needs to find the cosine of an angle that is twice as large as a known angle. The values for the sine and cosine of the original angle are placed in the formula to calculate the final result.

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Most popular questions from this chapter

Use words to describe the formula for each of the following: the cosine of the difference of two angles.

Use a graphing utility to approximate the solutions of each equation in the interval \([0,2 \pi) .\) Round to the nearest hundredth of a radian. $$ \cos x=x $$

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. $$ \sin 2 x+\sin x=0 $$

Use a calculator to solve each equation, correct to four decimal places, on the interval \([0,2 \pi)\) $$ 3 \cos ^{2} x-8 \cos x-3=0 $$

solve each equation on the interval \([0,2 \pi) .\) \(2 \cos ^{3} x+\cos ^{2} x-2 \cos x-1=0\) (Hint: Use factoring by grouping.)
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