Chapter 14.7, Problem 1LC

Solution

To Find: The value of $\sin 120°$ using double angle identity.

The value of the expression is $\sin 120°=\frac{\sqrt{3}}{2}$ .

Given information:

The trigonimetric expression $\sin 120°$ .

Concept and Formula Used:

Use the trigonometric identity $\sin 2A=2\sin A\cos A$ .

Calculation:

The given expression is $\sin 120°$

This can be written as

  $\sin 120°=\sin (2\cdot 60)°$

Using the identity $\sin 2A=2\sin A\cos A$

and simplify:

  $\begin{array}{l}\sin 120°=2\sin 60°\cos 60°\\ \sin 120°=2\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{2}\right)\\ \sin 120°=\frac{\sqrt{3}}{2}\end{array}$

Conclusion:

The value of the expression is $\sin 120°=\frac{\sqrt{3}}{2}$ .