What is the slope of the tangent line to y=cos(x)-2 at x=pi/2 ?

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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 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.

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