Question

Find each exact value if 0
Sin (x - y) if cos x = 8/17 and cos y = 3/5

Answer 1

Answer: 13/85

Work Shown:

If cos(x) = 8/17, then sin(x) = 15/17. Use the identity
`\sin^2(\text{x}) + \cos^2(\text{x}) = 1` to determine this.

If cos(y) = 3/5, then sin(y) = 4/5 using that same identity.

So,

sin(x-y) = sin(x)cos(y) - cos(x)sin(y)

sin(x-y) = (15/17)*(3/5) - (8/17)*(4/5)

sin(x-y) = 45/85 - 32/85

sin(x-y) = (45 - 32)/85

sin(x-y) = 13/85