Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \cos\left(\frac{2 \pi}{3}\right) = -\frac{1}{2} \)
Solution
Calculate or simplify the expression \( \cos\left(\frac{2 \pi}{3}\right) \).
Calculate the value by following steps:
- step0: Calculate:
\(\cos\left(\frac{2\pi }{3}\right)\)
- step1: Rewrite the expression:
\(-\cos\left(\frac{\pi }{3}\right)\)
- step2: Calculate:
\(-\frac{1}{2}\)
The value of \( \cos \left(\frac{2 \pi}{3}\right) \) is \( -\frac{1}{2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To solve \( \cos \left(\frac{2 \pi}{3}\right) \), we can visualize this on the unit circle. The angle \( \frac{2 \pi}{3} \) radians is located in the second quadrant, where cosine values are negative. The reference angle is \( \pi - \frac{2\pi}{3} = \frac{\pi}{3} \), and since \( \cos(\frac{\pi}{3}) = \frac{1}{2} \), we find \( \cos \left(\frac{2 \pi}{3}\right) = -\frac{1}{2} \). On a fun note, if angles were people at a party, \( \frac{2 \pi}{3} \) would definitely be the wallflower in the second quadrant, holding a drink and trying to avoid eye contact with the x-axis!
