Posted by Hannah on .
Find the exact value of the trigonometric function given that
sin u = 5/13 and cos = 3/5
1) sin(uv)
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.

Math 
Reiny,
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(AB) = sinAcosB  cosAsinB
then sin(uv) = sinucosv  cosusinv
= (5/13)(3/5)  (12/13)(4/5) = 63/65 
Math 
Hannah,
Thank You