Question

Find the exact value of sin(u-v) given that sin u= 5/13 and sin v= 12/13

with u and vin quadrant I.
sin(u - v) =
(Type an integer or a simplified fraction.)

Answer 1

Sin(u-v)= (-119/169)

Explanation:

Sin(a-b)= Sinacosb-cosasinb

Sin(u-v)= sinucosv-cosusinv

Sinu= 5/13

U = sin^-1(5/13)

U= 22.62

Sinv= 12/13

V= sin^-1(12/13)

V= 67.38

Fr right angle triangle

If sin u = 5/13

Cos u = 12/13

If sin v = 12/13

Cos v= 5/13

Sin(u-v)= sinucosv-cosusinv

Sin(u-v)=(5/13)*(5/13) -(12/13)*(12/13)

Sin(u-v)= 25/169 - 144/169

Sin(u-v) = (25-144)/169

Sin(u-v)= (-119/169)