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.cot(5θ + 2°) = tan(2θ + 4°)

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 trigonometric equation is the cotangent of seven alpha plus eight degrees is equal to the tangent of for alpha plus five degrees. Our answer choices are answer choice, a 77 degrees. Answer choice B seven degrees, answer choice C one degree and answer choice. D 77 divided by three degrees. All right. Cotangent and tangent are co functions. So this equation is true if the sum of our two angles is equal to 90 degrees. So if cotangents angle seven alpha plus eight degrees is added to tangents angle four alpha plus five degrees, we set that equal to 90 degrees. And then we solve for alpha and that's our solution. All right. So we can begin by combining like terms, we have the seven alpha plus the four alpha. That's 11 alpha and we have eight degrees plus five degrees, that's plus 13 degrees and equal to 90 degrees. Now solving for alpha, we can subtract 13 degrees from both sides on the left, we're left with 11 alpha that equals on the right, 90 degrees minus 13 degrees is 77 degrees, dividing both sides by 11. And we get our alpha equal to 77 degrees divided by 11 is seven degrees. There's our solution. We look at our answer choices and this matches with answer choice. B well 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.cot(5θ + 2°) = tan(2θ + 4°)

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