Question

The point P(0.5, 0) lies on the curve y-cos πx. If Q is the point (x, cos πχ), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

(i) 0
(ii) 0.4
(iii) 0.49
(iv) 0.499
(v) 1
(vi) 0.6
(vii) 0.51
(viii) 0.501

Answer 1

To find the slope of the secant line PQ, substitute the given values of x and π into the equation y = cos(πx) to find the y-coordinate of point Q. Calculate the difference in y-coordinates and x-coordinates between points P and Q, and divide the difference in y-coordinates by the difference in x-coordinates. Use a calculator to compute the slope for each given value of x.

Step-by-step explanation:

The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. To find the slope of the secant line PQ, we need to find the slope of the line passing through points P and Q. Substitute the given values of x and π into the equation y = cos(πx) to find the y-coordinate of point Q. Then calculate the difference in y-coordinates between points P and Q and the difference in x-coordinates. Finally, divide the difference in y-coordinates by the difference in x-coordinates. Using a calculator, compute the slope for each given value of x.