Find the exact value of the trigonometric function given that

Question

sin u = 5/13 and cos = -3/5

1) sin(u-v)

My teacher said to make two right triangles and then find the missing parts by the pyth theorem.

For the 5/13 triangle I got 12 and the other triangle I got 4. I do not know what to do now.

Answer 1

so the angle u could be in quadrant I inside a 5:12:13 triangle, with 13 as the hypotenuse,
so cos u = 12/13

angle v could be in quadrants II or III and are inside the 3:4:5 triangle , with 5 the hypotenuse, so
sin v = 4/5
draw the triangle in quadrant II with those dimensions

You must by now have learned that
sin(A-B) = sinAcosB - cosAsinB

then sin(u-v) = sinucosv - cosusinv
= (5/13)(-3/5) - (12/13)(4/5) = -63/65

Answer 2

Thank You