How do you find the exact value of sin(u+v) given that sinu=5/13 and cosv=-3/5?

1 Answer
Apr 8, 2017

-63/65 or 33/65

Explanation:

Since

sin(u+v)=sinucosv+cosusinv,

you would get cosu and sinv before applying it:

cosu=+-sqrt(1-sin^2u)=+-sqrt(1-25/169)=+-sqrt(144/169)=+-12/13

and

sinv=+-sqrt(1-cos^2v)=+-sqrt(1-(-3/5)^2)=+-sqrt(16/25)=+-4/5

Then

sin(u+v)=sinucosv+cosusinv=5/13*(-3/5)+-12/13*(+-4/5)=-15/65+-48/65
Then

sin(u+v)=(-15-48)/65=-63/65

or

sin(u+v)=(-15+48)/65=33/65