Given tan(2x) = -5/12, 2x is in quadrant II, find sin(x).

Question

I have been at this problem forever and got to the point where sinxcosx = 5/26. How do I go further? Any help appreciated.

Answer 1

2x=arctan(-5/12)

x=arctan(-5/12)/2

sin(x)= sin(arctan(-5/12)/2)

 

Use the half angle formula for sine sqrt((1-cos(A)/2))

 

sqrt((1-cos(arctan(-5/12))/2)

 

To compute cos(arctan(-5/12)) you must construct the triangle and find the cosine ratio of it which is 12/13. The thirteen coming from the pythagorean theorem. 

 

sqrt((1-12/13)/2)= sqrt(1/26)

 

So, sin(x)=1/sqrt(26)