Question

if sin theta =1/2 and theta is acute , then the value sin 2theta =

Answer 1

Given,

$\[\sin \theta = \frac{1}{2}\]$

The angle $\[\theta \]$ is an acute angle.

Solution,

Calculate the value of $\[\theta \].$

$\[\begin{array}{l} \Rightarrow \sin \theta = \frac{1}{2}\\ \Rightarrow \sin \theta = \sin 30^\circ \\ \Rightarrow \theta = 30^\circ \end{array}\]$

Calculate the value of $\[\sin 2\theta .\]$

$\[\begin{array}{l} \Rightarrow \sin 2\theta \\ \Rightarrow \sin \left( {2 \times 30^\circ } \right)\\ \Rightarrow \sin \left( {60^\circ } \right)\\ \Rightarrow \frac{{\sqrt 3 }}{2}\end{array}\]$

Hence, the value of $\[\sin 2\theta \]$ is $\[\frac{{\sqrt 3 }}{2}\].$

Answer 2

If sin θ = 1/2 and θ is acute, then the value of the sin 2θ is​ √3 / 2  and value of  sin²θ  is 1/4

Given:

• θ is acute
• sin θ = 1/2

To Find:

• Value of  Sin 2θ
• Value of sin²θ

Solution:

Acute angles:

Angles whose measures are between 0° and 90°

Step 1:

Solve for θ using sin 30° = 1/2

sin θ = 1/2

=> θ = 30°

Step 2:

Solve for sin 2θ using θ = 30°

sin 2θ = sin (2 x 30°)

=> sin 2θ =   sin 60°

=> sin 2θ = √3 / 2

Step 3:

Solve for sin²θ using sin θ = 1/2

sin²θ = (1/2)²

=> sin²θ =   1/4

If sin θ = 1/2 and θ is acute, then the value of the sin 2θ is​ √3 / 2  and value of  sin²θ  is 1/4

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