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 = opposite side over hypotenuse = o/h, o=4, h=5. adjacent side = -3= a

in quadrant II, all trig functions are <0, except sines and cosecants.

secu = 1/sinu = 5/4

cosu = a/h = -3/5

secu = h/a = -5/3

tan u = o/a = 4/-3 = -4/3

cotu = a/o = -3/4

cosv = -7/25

secv =-25/7

It's a 7-24-25 right triangle 25^2 = 24^2 + 7^2

sinv = 24/25

cscv = 25/24

tanv = 24/-7 = -24/7

cotv = -7/24