The slope of the tangent line means derivative. So, take the derivative of y = cosx - 2, and get dy/dx = -sinx. Evaluate at pi/2, and -sin(pi/2) = -1. So the slope of the tangent line at that point is -1.
The slope of the tangent to the curve defined by y=cos(x)-2 at the point where x=pi/2 is required.
For a curve y = f(x), the slope of the tangent at x = a is equal to y'(a).
For y = cos x - 2, y' = -sin x
At x = pi/2, y' = 1
The required slope of the tangent is 1.
The gradient of the tangent to the curve at any point is given by dy/dx. Get the slope of the equation, which is about -sinx. Subsitute in x= pi/2 and also inside -sinx in radian form, so the slope or the gradient of the tangent line is -1.