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.tan α = cot(α + 10°)

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 tangent of alpha equals the co tangent of alpha plus 23 degrees. Our answer choices are answer choice. A 33.5 degrees. Answer choice B 67 degrees. Answer choice C 11.5 degrees and answer choice D 23 degrees. All right, tangent and cotangent are co functions. So this statement is true if the sum of their angles equals 90 degrees, so we can take tangents angle which is alpha and add that to cotangents angle which is alpha plus 23 degrees set that equal to 90 degrees. And then solve for alpha. So we can start off combining like terms alpha plus alpha is two alpha. Break down plus 23 degrees equals 90 degrees. We can subtract 23 degrees from both sides on the left. We've got two alpha and that equals on the right, 90 degrees minus 23 degrees is 67 degrees. Now dividing both sides by two on the left, we have alpha that equals on the right 67 degrees, divided by two is 33.5 degrees. And there's our solution, we look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Struggling with Trigonometry?

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.tan α = cot(α + 10°)

Watch next

Trigonometric Functions on the Unit Circle practice set