Question

If x and y are in the interval (0,π/12) and sin x = 3/5 and cos y = 12/13, evaluate:

sin (x-y)

I started by trying to find the value of x and y and i got 0.645 and 0.394. And I substituted the values in and got 0.2461 etc. But the answer at the back of the book says 16/65. Which is 0.2461 etc however I am supposed to find it in a fraction. How can I do that?

Answer 1

You can't just plug those numbers in. You must use the Sum and Difference Identities. It will be helpful to memorize the equation:

sin(A-B) = sinA * cos B - cos A * sin B

You are given two of the numbers you need. Use the #1 Identity, sin^2(x) + cos^(2)x = 1, to find sin y and cos x. Then, just plug & chug.

Answer 2

find the length of each arc of 12 yards and 260 degrees