What is the exact value of sin (120 degrees)?Question 31Select one:a.½b..866c.√3/2d.-1/2e.None of these

Break Down the Problem

1. Identify the angle: 120 degrees.
2. Recognize that 120 degrees is in the second quadrant of the unit circle.
3. Determine the reference angle.

Relevant Concepts

1. The reference angle for 120 degrees is $180^\circ - 120^\circ = 60^\circ$.
2. The sine function is positive in the second quadrant.

Analysis and Detail

1. We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$.
2. Thus, $\sin(120^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2}$.

Verify and Summarize

• The sine of 120 degrees is derived by recognizing it is in the second quadrant and using the reference angle to find that $\sin(120^\circ) = \frac{\sqrt{3}}{2}$.

Final Answer

The exact value of $\sin(120^\circ)$ is $\frac{\sqrt{3}}{2}$, corresponding to option c.