Question

Given sin y = -4/5, where π < y < 3π/2, and cos x = 12/13, where 0 < x < π/2. Find the exact value of sin (x - y).

Please show all the exact steps in order I am really lost on how to solve this.

Answer 1

Solution given:

sin y = -4/5

p/h=4/5

p=4

h=5

b=√{5²-4²)=3

cos y = b/h=-3/5

again

cos x=12/13

b/h=12/13

b=12

h=13

p=√(13²-12²)=5

sin x=p/h=5/13

now

sin[x-y]=sinxcosy-cosxsiny

=5/13×-3/5-(12/13×-4/5)=33/65 is your answer.