6.3.3 Sketching Graphs of Trigonometric Functions (Part 2)


6.3.3 Sketching 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 2 x + cos x = 0 for 0 ≤ x 2π.
State the number of solutions.

Solution:
(a)



(b)




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

The suitable graph to draw is y = π 4 x .  
x
π 2
π
2π
y = π 4 x
½
¼
From the graphs, there are two points of intersection for 0 ≤ x ≤ 2π.
Number of solutions = 2.


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