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?

1 Answer
Jun 20, 2017

(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