Find an example of a point (x,y) on the graph of f(x)=2cos⁡(x) where the tangent...

If u derivate the function f(x) u will have a function $[f^{\prime }(x)]$ that will give u the slope for any value of x:
so, the derivate of the function ${\displaystyle f\left(x\right)=2\cos \left(x\right)is{f}^{\prime }\left(x\right)=-2\sin \left(x\right)}$, now to evalute where the derivate is equal to 1 (the slope that are asking for).
${\displaystyle 1=-2\sin \left(x\right)\to {\sin }^{-1}\frac{-1}{2}=\frac{-\pi }{6}=-0.53}$
So the x,y coordinate are (-0.53 , 1.72)