Question
The value of sin 120 degree is
Answers
GPT-4o mini
The value of \(\sin 120^\circ\) can be calculated using the unit circle or the properties of trigonometric functions.
Since \(120^\circ\) is in the second quadrant, where sine is positive, we can also express \(120^\circ\) as:
\[
120^\circ = 180^\circ - 60^\circ
\]
Using the sine identity for angles, we have:
\[
\sin(180^\circ - \theta) = \sin(\theta)
\]
So,
\[
\sin(120^\circ) = \sin(60^\circ)
\]
The value of \(\sin(60^\circ)\) is \(\frac{\sqrt{3}}{2}\).
Therefore,
\[
\sin(120^\circ) = \frac{\sqrt{3}}{2}
\]
So, the value of \(\sin 120^\circ\) is \(\frac{\sqrt{3}}{2}\).
Since \(120^\circ\) is in the second quadrant, where sine is positive, we can also express \(120^\circ\) as:
\[
120^\circ = 180^\circ - 60^\circ
\]
Using the sine identity for angles, we have:
\[
\sin(180^\circ - \theta) = \sin(\theta)
\]
So,
\[
\sin(120^\circ) = \sin(60^\circ)
\]
The value of \(\sin(60^\circ)\) is \(\frac{\sqrt{3}}{2}\).
Therefore,
\[
\sin(120^\circ) = \frac{\sqrt{3}}{2}
\]
So, the value of \(\sin 120^\circ\) is \(\frac{\sqrt{3}}{2}\).