If tan2x = - 24/7, what are the values of sin x and cos x?

To avoid conflict of notation I'm going to replace your x by q






Cross multiply:



Distribute:



Get 0 on the right



Divide both sides through by -2



Factor



Use 0 factor property on the first factor:







This could either be in the 1st quadrant or the 3rd since
the tangent is positive in the 1st and 3rd quadrants.

So angle  could be either of these:



In either case r = 5













So we have



For the first graph , 
For the second graph , 


Use 0 factor property on the second factor:







This could either be in the 2nd quadrant or the 4th since
the tangent is negative in the 2nd and 4th quadrants.

So angle  could be either of these:



In either case r = 5













So we have



For the first graph , 
For the second graph , 

Edwin