SOLUTION: sin theta = 7/25 and 90 degrees < theta < 180 degrees find tan 2theta

Draw the angle in QII by drawing a right triangle in QII that
has an angle with sine of 7/25.

Since the sine is  make the opposite
side or y equal to the numerator of 7/25, which is 7, and the 
hypotenuse or r equal to the denominator of 7/25, or 25.  I will
indicate the angle by the red curved line.



Calculate the adjacent side or x by the Pythagorean theorem:













We take x as negative because x goes left in QII.



 


Since ,











The 12 goes into 576 48 times, so that simplifies to



Edwin