## 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?

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?

## Answers

# (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#

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