Question
Download Solution PDFFind the general solution of the equation 4 sin 3x = 2?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If sin θ = sin α then θ = nπ + (- 1)n α, α ∈ [-π/2, π/2], n ∈ Z.
|
T-Ratios |
0° |
30° |
45° |
60° |
90° |
|
Sin |
0 |
1/2 |
1/√2 |
√3/2 |
1 |
|
Cos |
1 |
√3/2 |
1/√2 |
1/2 |
0 |
|
Tan |
0 |
1/√3 |
1 |
√3 |
Not defined |
Calculation:
Given: 4 sin 3x = 2
⇒ sin 3x = ½
As we know that, sin (π/6) = ½
⇒ sin 3x = sin (π/6)
As we know that, if sin θ = sin α then
θ = nπ + (- 1)n α, α ∈ [-π/2, π/2], n ∈ Z.
⇒ 3x = nπ + (- 1)n × (π/6), where n ∈ Z.
⇒ x = n × (π/3) + (- 1)n × (π/18), where n ∈ Z.Last updated on May 30, 2025
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