Find the exact values (precalc)

Question

Find the exact values (fractions) for the trigonometric expression given that sin u = 4/5 and cos v = -7/25 (both u and v are in II quadrant)

Answer 1

sinu = 4/5 cosu=3/5 it's a 3-4-5 right triangle. 9+16 =25

cosv =-7/25 sinv = 24/25 it's a 7-24,-26 right triangle 7^2 + 24^2 = 25^2

cos(u+v) = cosucosv - sinusinv = (3/5)(-7/25) - (4/5)(24/25) = (-21)/125 -96/125 = -117/125

use the sin(u+v) formula, plug in the fractions

if you want tan(u+v) that = sin(u+v)/cos(u+v)