Find one solution for each equation. Assume all angles involved a...

Question

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.

sin(2θ + 10°) = cos(3θ - 20°)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve the following trigonometric equation consider all the angles as acute angles. Our equation is the sine of five alpha plus 18 degrees equals the cosine of four alpha minus 27 degrees. Our answer choices are answer choice, A 99 degrees. Answer choice B 45 degrees. Answer choice C 35 degrees and answer choice D 11 degrees. All right. Sine and cosine are co functions. So this equation is true if the sum of the two angles is equal to 90 degrees, so we can take those two angles, add them together, set it equal to 90 degrees and then solve for alpha to find our solution. So we'll take the first angle sines angle five alpha plus 18 degrees and add that to cosine's angle for alpha minus 27 degrees. Set that equal to 90 degrees to solve for alpha will start by combining like terms. So we have a five alpha plus four alpha which is nine alpha and then combining the 18 degrees minus 27 degrees, that's minus nine degrees still equal to 90 degrees. Now, we can add nine degrees to both sides. And on the left, we have nine alpha that's equal to on the right, 90 degrees plus nine degrees is 99 degrees. Now, dividing both sides by nine. On the left, we have alpha equals on the right, 99 degrees divided by nine is 11 degrees. And there's our solution, we look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sin(2θ + 10°) = cos(3θ - 20°)

Key Concepts

Trigonometric Identities

Angle Addition Formulas

Acute Angles

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