draw the graph of cos x
Answers
Step-by-step explanation:
Steps to draw the graph of y = c cos ax.
Steps I: Obtain the values of a and c.
Step II: Draw the graph of y = cos x and mark the points where y = cos x crosses x-axis.
Step III: Divide the x-coordinate of the points where y = cos x crosses x-axis by a and mark maximum and minimum values of y = c cos ax as c and –c on y-axis.
The graph obtained is the required graph of y = c cos ax.
Properties of y = cos x.
(i) The graph of the function y = cos x is continuous and extends on either side in symmetrical wave form.
(ii) Since the graph of y = cos x intersects the x-axis at the origin and at points where x is an odd multiple of 90°, hence cos x is zero at x = (2n + 1)π2 where n = 0, ±1, ±2, ±3, ±4, ……………... .
(iii) The ordinate of any point on the graph alwa
ys lies between 1 and - 1 i.e., - 1 ≤ y ≤ 1 or, -1 ≤ cos x ≤ 1 hence, the maximum value of cos x is 1 and its minimum value is - 1 and these values occur alternately at x = 0, π, 2π,……… i. e., at x = nπ, where n = 0, ±1, ±2, ±3, ±4, ……………...
(iv) The portion of the graph between 0 to 2π is repeated over and over again on either side, since the function y = cos x is periodic of period 2π