Question

Find the exact value for tan theta given cos(2theta)=120over 169 and 2 theta lies in quadrant 4

Answer 1

This is probably not correct, but if you have been working with these, maybe some of it will make sense and we can come to the correct answer together. I replaced the cos2theta with an identity: 1 - sin^2 theta = 120/169. I subtracted 1 from both sides and changed it to 169/169. Then I had -sin^2 theta = 120/169 - 169/169. Doing the math I got -sin^2 theta = -49/169. Since both sides are negative they are the same as positive. Then I took the square root of both sides and got sin theta = 7/13. This is the part that kind of confused me. If the angle is in the 4th quadrant, the 7 is negative (y is negative in the 4th Q). So using Pythagorean's theorem I got the missing side to be the square root of 120. Finding the tangent of this gives us -7/2sqrt30. That's the best I can do; I think it's a good start.