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.cos(2θ + 50°) = sin(2θ - 20°)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to solve the following trigonometric equation. Consider all the angles as acute angles. Our equation is the cosine of eight alpha plus 87 degrees equals the sign of five alpha minus 49 degrees. Our answer choices are answer choice. A 52 degrees. Answer choice B 25 degrees. Answer choice C four degrees and answer choice. D 136 divided by three degrees. All right. So cosine and sine are co functions. So this statement is true if the angles add up to 90 degrees, so we can take cosine's angle, eight alpha plus 87 degrees and add that to sines angle which is five alpha minus 49 degrees and set that equal to 90 degrees. Then we solve for alpha and that's our solution. So now we can combine like terms eight alpha plus five alpha is 13 alpha and 87 degrees minus 49 degrees is plus 38 degrees. Those together add up to 90 degrees. Solving for alpha will subtract 38 degrees from both sides. On the left, we have 13 alpha that's equal to on the right, 90 degrees minus 38 degrees is 52 degrees. Now, dividing both sides by 13 on the left, we have alpha equals on the right. 52 degrees divided by 13 degrees is four degrees. And that's our solution. Alpha equals four degrees. We look at our answer choices and this matches with answer choice. See while done, we'll catch you on the next one.

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Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.cos(2θ + 50°) = sin(2θ - 20°)

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