Question

Find theta if 2 sin 2 theta =√ 3


Do give general solution of theta.

Thanks! Do try to explain your answer. ( Though it's a question of 11,12th classes, Do explain as if you are explaining to 10th student)

Answer 1

Answer:

θ = (π/6) ± πn, (π/3) ± πn

Step-by-step explanation:

Given Equation is 2 sin 2θ = √3

⇒ sin 2θ = √3/2.

The sin function is positive in the first and second quadrant. We have to subtract the reference angle from π to find the solution in 2nd quadrant.

In first Quadrant, √3/2 = sin(π/3)

In Second Quadrant, √3/2 = sin(π/3) = sin(π - π/3) = sin(2π/3).

So, the solutions are 2θ = π/3 and 2θ = 2π/3.

∴ General solutions of sin(2θ) = (π/3) + 2πn (or) 2θ = (2π/3) + 2πn

θ = (π/6) ± πn, (π/3) ± πn.

Hop it helps!

Answer 2

Question:

2 sin 2 theta =√ 3

Method of Solution:

Here, Sin2∅=√3/2 , [it is , In the group of ∅ Third Quadrant or Fourth Quadrant.

Statement: Give general solution of theta.

Equation : 2 Sin2∅= √3

2Sin2∅ = √3

Sin2∅ =√3/2

Sin 2∅ = Sin (√3/2)

Note; π is Equal to 180° , So we can write as

Sin 2∅ = Sin (√3/2)

Sin 2∅= Sin ( π/3)

Here, Sin is cancelled on Both Sides, So we get,

2∅=(π/3)

∅ = (π/6)

Here, We need to remember Something!

Note:

First :( Positive) (Sin, Cos , Cosec, tan , cot ,sec)

Second: ( Positive), Sin , Cosec with (180°-x)

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[∅ = 180/6+ 180n , 180°/3 + 180n ] Where n denotes General Solution!

We are already know that π = 180, Then replace it!

[∅ = 180/6+ 180n , 180°/3 + 180n ]

[∅= π/6 ± πn , π/3  πn ]

Hence, General Solution for theta :    π/6 ± πn , π/3  πn

Hence , General Solution of theta is π/6  ±πn , π/3  πn , Where n represent General Solution!

Thanks!!✔✔