working with sum and difference formuas

Question

sin (u-v)......... sin u=8/17 sin v =3/5

Answer 1

Hi Lu,

The formula for sin(u±v) is sin(u)cos(v)±sin(v)cos(u)

In this case, it's sin(u-v) so we'll use sin(u)cos(v)-sin(v)cos(u)

Plugging in for sin(u) and sin(v) gives:

(8/17)cos(v) - (3/5)cos(u)

To find cos(v) and cos(u), construct the triangles from the sin info

Doing this I get cos(u) = 15/17, and cos(v) = 4/5

So the final answer is:

(8/17)(4/5) - (3/5)(15/17) = -(13/85), or -0.153

Hope that helps!

Answer 2

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

Then you need to compute the two cosines...15/17 and 4/5 and substitute.

Use Pythagorean theorem to get the cosines...unless you recognize that one triangle is 8-15-17 and the other is 3-4-5.