SOLUTION: If t=tan(x) what is 1-sin(2x)?

Algebra ->  Trigonometry-basics -> SOLUTION: If t=tan(x) what is 1-sin(2x)?       Log On


   



Question 1143228: If t=tan(x) what is 1-sin(2x)?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

If t+=+tan%28x%29 what is 1-sin%282x%29?

We draw a right triangle. The tangent of x is t, which is the 
same as t/1.  The tangent is the opposite side over tha adjacent side,
so we make the opposite side of angle x be the numerator of t/1
which is t and the adjacent side be the denominator of t/1 which
is 1.  That makes the hypotenuse be sqrt%281%5E2%2Bt%5E2%29 or sqrt%281%2Bt%5E2%29. 



The sine is the opposite over the hypotenuse and the cosine is the
adjacent over the hypotenuse, so



Edwin