1. ## Trigonometry Questions

Hello, I've got a few questions that I need help with. I'm not sure how to do these, and any help is appreciated!

1) Solve algebraically the equation √3tan2x = 1, for 0 <= x <= Pi.
2) By expanding cos(x+y) show that the exact value of cos(x+y) is 3/5, where sinx = 7/25, and cosx = 20/25.
3) Solve the equation sinx°cos20° - cosx°sin20° = 4/9 for 0 < x < 180.

2. ## Re: Trigonometry Questions

Originally Posted by Influence
Hello, I've got a few questions that I need help with. I'm not sure how to do these, and any help is appreciated!

1) Solve algebraically the equation √3tan2x = 1, for 0 <= x <= Pi.
Tan2x is like y at the start. If √3 y =1, then y =1/√3.
So tan2x =1/√3. Now tan of what angle equals 1/√3. Let 2x equal that number. Then divide by 2.

3. ## Re: Trigonometry Questions

Originally Posted by JaguarXJS
Tan2x is like y at the start. If √3 y =1, then y =1/√3.
So tan2x =1/√3. Now tan of what angle equals 1/√3. Let 2x equal that number. Then divide by 2.
Ah, that makes sense! I just tried that, and got the answer that it was wanting! Thanks a lot! Have you got any idea how to do the other two??

4. ## Re: Trigonometry Questions

Originally Posted by Influence
2) By expanding cos(x+y) show that the exact value of cos(x+y) is 3/5, where sinx = 7/25, and cosx = 20/25.
First I assume you have a typo and that cosy = 20/25. cos(x+y) = cosxcosy-sinxsiny. You have the exact values of sinx and cosy. Now draw 2 right triangles, one using an angle x and another using angle y. Find the length of all sides. 4 sides are basically given to you. How do you thing you find the other 2 sides?

5. ## Re: Trigonometry Questions

Originally Posted by JaguarXJS
First I assume you have a typo and that cosy = 20/25. cos(x+y) = cosxcosy-sinxsiny. You have the exact values of sinx and cosy. Now draw 2 right triangles, one using an angle x and another using angle y. Find the length of all sides. 4 sides are basically given to you. How do you thing you find the other 2 sides?
Yeah, sorry, that's a typo. I've used Pythagoras theorem to find the missing sides. On the sinx triangle, the missing side has a length of 24, and on the cosy triangle the missing side is 15? So, I'm guessing all I do now is use these values, along with the cosxcosy-sinxsiny equation, and use that to get my answer??