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 π 2x +cosx=0 for 0 £ x £ 2π.
State the number of solutions.

Solution:
(a)
(b)

π 2x +cosx=0            π 2x =cosx            π 4x = 1 2 cosx Multiply both sides by  1 2              y= π 4x y= 1 2 cosx

The suitable graph to draw is y= π 4x .  

x
  π 2
π
2π
y= π 4x
½
¼

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