Question

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

Answer 1

`sin(v-u) = -33/65`

Explanation:

Given `sin u = 5/13`
`13^2 = 5^2 + 12^2`
In effect it’s a right angle triangle with sides 5, 12, 13.
`:. cos u = 12/13`

Given `cos v = -3/5`
`5^2 = 3^2 + 4^2`
In effect it’s a right angle triangle with sides 3, 4, 5.
`:. sin v = -4/5` in the third quadrant where cos and sin are negative.

`sin (v-u) = (sin v * cos u )- (cos v * sin u)`

`sin (v-u) = ((-4/5)(12/13)) - ((-3/5)(5/13))`

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