Question
sin 240° = (1 point) Responses −3√2 negative the fraction with numerator square root of 3 and denominator 2 12 1 half 3√2 the fraction with numerator square root of 3 and denominator 2 − 2√2
Answers
Answered by
GPT-4o mini
To find \(\sin 240^\circ\), we first recognize that 240° is in the third quadrant. The reference angle for 240° is calculated as:
\[
240^\circ - 180^\circ = 60^\circ
\]
In the third quadrant, the sine function is negative. Therefore, we can express \(\sin 240^\circ\) as:
\[
\sin 240^\circ = -\sin 60^\circ
\]
We know from trigonometric values that:
\[
\sin 60^\circ = \frac{\sqrt{3}}{2}
\]
So, we have:
\[
\sin 240^\circ = -\frac{\sqrt{3}}{2}
\]
Looking at the provided responses:
- The fraction with numerator square root of 3 and denominator 2 (-\(\frac{\sqrt{3}}{2}\))
This matches our derived value.
Therefore, the answer is:
\[
-\frac{\sqrt{3}}{2}
\]
\[
240^\circ - 180^\circ = 60^\circ
\]
In the third quadrant, the sine function is negative. Therefore, we can express \(\sin 240^\circ\) as:
\[
\sin 240^\circ = -\sin 60^\circ
\]
We know from trigonometric values that:
\[
\sin 60^\circ = \frac{\sqrt{3}}{2}
\]
So, we have:
\[
\sin 240^\circ = -\frac{\sqrt{3}}{2}
\]
Looking at the provided responses:
- The fraction with numerator square root of 3 and denominator 2 (-\(\frac{\sqrt{3}}{2}\))
This matches our derived value.
Therefore, the answer is:
\[
-\frac{\sqrt{3}}{2}
\]