If sin x = - 4/5 where pi < x < (3pi)/2 and cos y = 8/17 where 0 < y < n/2 , find any two of the following: either sin(x - y), cos(x - y) , or tan(x - y) .

The answer is

sin(x-y)= 13/85

cos(x-y)= -36/85

What we know.

The intervals mean that all values of x are in the 3rd quadrant. The second one mean that all y values are in the 1st quadrant.

Let find sin( x-y).

We can find sin of y.

Remeber that all y values are in the 1st quadrant. This means y is positive.

We can find cos x by doing the exact opposite.

We know that sin x=-4/5 so we need to find the adjacent/hypotenuse side.

Remember cosine in the 3rd quadrant is negative so

cos x=-3/5.

Plug the values into the earlier formula,

Multiply the fractions then multiply it

For cos(x-y).

Plug in the same ones for earlier,

the answer is 62.8 cubic units