Question
Select your answer Simplify \( \sec \left(\frac{2 \pi}{3}\right) \) \( -\infty \) -2 2
Ask by Cox Gross. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value is -2.
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Beyond the Answer
To simplify \( \sec \left(\frac{2 \pi}{3}\right) \), we first express secant in terms of cosine: \( \sec(x) = \frac{1}{\cos(x)} \). The angle \( \frac{2 \pi}{3} \) is in the second quadrant, where cosine is negative. In fact, \( \cos\left(\frac{2 \pi}{3}\right) = -\frac{1}{2} \). Therefore, \( \sec\left(\frac{2 \pi}{3}\right) = \frac{1}{-\frac{1}{2}} = -2 \). The answer is \( -2 \). So, the correct answer is \( -2 \).
