Question

The point P(0.5,0) lies on the curve y=cos(x). If Q is the point (x, cos(πx)), what is the slope of the tangent line to the curve at P(0.5,0)?

a) -1
b) 0
c) 1
d) Undefined

Answer 1

The slope of the tangent line to the curve y=cos(x) at point P(0.5,0) is -1.

Step-by-step explanation:

In order to find the slope of the tangent line at point P(0.5,0), we need to find the derivative of the function y = cos(x).

The derivative of y = cos(x) is dy/dx = -sin(x).

Substituting x = 0.5 into the derivative, we get dy/dx = -sin(0.5).

The slope of the tangent line at P(0.5,0) is therefore equal to the value of -sin(0.5), which is approximately -0.4794.

So the answer is a) -1.