Question

How do you find the exact value of `sin(alpha-beta)` if `sinalpha=-5/13` and `sinbeta=1/6` if the terminal side of `alpha` lies in QIII and the terminal side of `beta` lies in QI?

Answer 1

`(12 - 5 sqrt 35)/78 = 0.225`

Explanation:

`sin alpha = -5/13` since `alpha` lie in QIII, therefore `cos alpha = -12/13 and tan alpha = 5/12`

`sin beta = 1/6` since `beta` lie in QI, therefore `cos beta = sqrt 35/6 and tan alpha = 1/sqrt 35`

`sin (alpha - beta) = sin alpha cos beta - sin beta cos alpha` `->i`

plug in the above values in `->i`

`sin (alpha - beta) = (-5/13)( sqrt 35/6) - (1/6)( -12/13)`

`sin (alpha - beta) = (-5sqrt 35)/78 + 12/78 = (12 - 5 sqrt 35)/78 = 0.225`