SOLUTION: Given cos (theta/2) = a and sin (2 theta) = b, find tan (theta)

Algebra ->  Trigonometry-basics -> SOLUTION: Given cos (theta/2) = a and sin (2 theta) = b, find tan (theta)       Log On


   

Question 1128743: Given cos (theta/2) = a and sin (2 theta) = b, find tan (theta)
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  If   cos%28theta%2F2%29 = a,  then  cos%28theta%29 = 2%2Acos%5E2%28theta%2F2%29-1 = 2%2Aa%5E2-1.        (1)



2.  If  sin%282%2Atheta%29 = b,  then  2%2Asin%28theta%29%2Acos%28theta%29 = b,

    hence,  sin%28theta%29 = b%2F%282%2Acos%28theta%29%29 = (substitute from (1)) = b%2F%282%2A%282%2Aa%5E2-1%29%29.



3.  Then  tan%28theta%29 = sin%28theta%29%2Fcos%28theta%29 = b%2F%282%2A%282%2Aa%5E2-1%29%29 : %282a%5E2-1%29%29 = b%2F%282%2A%282a%5E2-1%29%5E2%29.        ANSWER

Solved.