Hans Herland
- 17
- 1
Homework Statement
Firstly, sorry for the probably weird title. I have no idea how to title this problem, but hopefully my explanation is better. =)
Given $$cos x = \frac {2\sqrt{ab}} {a + b},$$ where x is in the first quadrant and a + b ≠ 0, ab > 0.
Calculate sin x expressed by a and b.
Homework Equations
Sine formula
Pythagorean theorem
The Attempt at a Solution
Now I've come up with what I think is a solution, but for some reason it feels weird, and like I'm not thinking correctly when it comes to the task.
I used Pythagorean theorem combined with the information is given in the cos-equation.
If ##2\sqrt{ab}## is a side, B, of a triangle, and ##a + b## is the hypotenuse, then the last side, C, of the triangle should be:
$$C = \sqrt {(a+b)^2-(2\sqrt{ab})^2}$$
Using this in the sine formula, I get the following:
$$sin x = \frac {\sqrt{(a+b)^2-(2\sqrt{ab})^2}} {a+b}$$
So the question is, does this sound like a reasonable answer to this problem, or am I misunderstanding what I'm supposed to do?
Thanks for any help. =)