Sum and Diff Formulas

Question

Find the exact value of sin(a-b) if sin a=5/13 and sin b = 4/5 if a and b are between 0 and pi/2

Answer 1

Draw two triangles:

Everything is positive because you are told the angles are in the first quadrant. You will get one triangle with sides 5,12,13 and one with sides 3,4,5 (these are well known Pythagorean Triples)

From those triangles you can get cos(a) and cos(b), which you will need in the angle difference formula.

sin (a-b) = sin(a) * cos(b) - cos(a) * sin(b)

With trig, always think about drawing triangles!