Question

Find the exact value of the trigonometric function give that sin u=5/13 and cos v= -3/5: sin(u-v)

Answer 1

Recall the identity \(\large \sin(u-v) = \sin u\cos v - \cos u\sin v\). Since you know \(\sin u=\dfrac{5}{13}\), you'll need to find \(\cos u\). Likewise, since you know \(\cos v = -\dfrac{3}{5}\), you'll need to find \(\sin v\). Once you find those values, substitute everything into the identity to get the desired answer.

Can you take things from here? :-)

Answer 2

So cos v= 12/13 and sin u=4/5
Plugging it into that identity makes it sin(4/5)cos(12/13)-cos(-3/5)sin(5/13)
I'm a bit stuck after that though. I feel like I'm having a blonde moment.