Finding stationary points

Googling (y^2+y-16)sin(x) will display the stationary points which may be of some help.

I already tried this and but it did not show them, thanks

It is solving the two equations to get the points that I need help with, I have solved one for y then placed that back in but my results do not seem right

Whenever a product equals 0, one or both of the multiplicand and multiplier must equal 0.

For what values of x does cos(x) = 0?
For what values of y does y^2 + y - 16 = 0?

Do the same for the second function.

Since the expressions in x don't share a zero, and the expressions in y don't share a zero, you're going to have to select an x from one function and a y from the other function.

Yeah but does cosx = 0 and sinx = 0 not have infinite solutions?
I was at first using x = pi/2 or 3pi/2 but realised there would be more values

Sorry I know I'm probly being stupid , I can solve for y but just cannot see how my answers are stationary points

Can't there be an infinite number of stationary points?