Find the exact value of the trig function below.

Question

sin(x-y) if sinx=7/25, cosx=24/25, siny=3/5, and cosy=4/5

Answer 1

I suggest using the trigonometric identity

 

sin(x - y) = sinx cosy - cosx siny = (7/25)(4/5) - (24/25)(3/5)

 

You can finish from here.

Answer 2

sin(x-y) = sin(x) * cos(y) - cos(x) * sin(y)

> The theroem of the broken chord leads us to the trig identity above

 

=  { (7 / 25) * (4 / 5) } - { (24 / 25) - (3 / 5) }

= {28 / 125} - {72 / 125}

= -44 / 125

 

In trigonometry, using the right formula at right place is the key.

 

 

Answer 3

cos(x-y)=cos(x)*cos(y)+sin(x)*sin(y)

=117/125

sin(x-y)=sin(x)*cos(y)-cos(x)*sin(y) =-44/125

Answer 4

Use the subtraction angle identity for sine.

 

sin(x - y) = sinxcosy - cosxsiny

 

You are given your values.  Just plug them in. 

 

 

Also, you will need to find       

 

sinx = √(1 - cos²x)

       = √[1 - (24/25)²]