Question
Mathematics Question on Trigonometric Equations
The number of solutions of |cos x | = sin x , such that -4π ≤ _x _≤ 4π is :
A
4
B
6
C
8
D
12
Answer
8
Explanation
Solution
Number of solutions of the equation |cos x | = sin x for x ∈ [-4π, 4π] will be equal to 4 times the number of solutions of the same equation for x ∈[0, 2π].
Graphs of y = |cos x | and y = sin x are as shown below.
Hence, two solutions of a given equation in [0, 2π]
⇒ Total of 8 solutions in [–4π, 4π].