Question
Download Solution PDFWhat is the length of the longest interval in which the function f(x) = 3sin x – 4sin3 x is increasing?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Trigonometric formulas used:
- sin 3x = 3sin x – 4sin3 x
Calculation:
Given: f(x) = 3sin x – 4sin3 x
We know that, sin 3x = 3sin x – 4sin3 x
So, f(x) = 3 sin x – 4 sin3 x = sin 3x
We know that, sin 3x is a periodic function.
As we know Sin x is a periodic function [-π/2 to π/2]
Since here the function is Sin 3x the range becomes [-π/6 to π/6]
So, sin 3x increases from –π/6 to π/6.
∴ The length of the increasing interval = π/6 – (-π/6) = π/3
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