5.3.2 To Sketch Graphs of Trigonometric Functions (Part 2)

5.3.2 To Sketch Graphs of Trigonometric Functions (Part 2)

Example 2:
(a) Sketch the graph y = –½ cos x for 0 £ x £ 2π.
(b) Hence, using the same axes, sketch a suitable graph to find the number of solutions to the equation $\frac{\pi }{2x}+\mathrm{cos}x=0$ for 0 £ x £ 2π.
State the number of solutions.

Solution:
(a)
(b)

The suitable graph to draw is $y=\frac{\pi }{4x}.$

 x $\frac{\pi }{2}$ π 2π $y=\frac{\pi }{4x}$ ½ ¼ ⅛

From the graphs, there are two points of intersection for 0 £ x £ 2π.
Number of solutions = 2.