Question

If `sinx=3/5,cosy=-(12)/(13),`where x and y both lie in second quadrant, find the value of `sin (x + y)dot`

Answer 1

Here, `sin x = 3/5`
So, `cosx = sqrt(1-(3/5)^2)=+-4/5`
As, x lies in 2nd quadrant, `cos x = -4/5`
Now, `cos y = -12/13`
So, `sin y = sqrt(1-(-12/13)^2)=+-5/13`
As, y lies in 2nd quadrant, `sin y = 5/13`
Now, we know,
`sin(x+y) = sinxcosy+cosxsiny`
`=3/5(-12/13)+(-4/5)(5/13) =-56/65`