Find the value of $x$ such that $cos(x) = -frac{1}{2}$ and $sin(x)$ is negative on the unit circle.
Answer 1
Abigail Nelson
To solve for $x$ such that $\cos(x) = -\frac{1}{2}$ and $\sin(x)$ is negative on the unit circle, follow these steps:
1. Identify the angles where $\cos(x) = -\frac{1}{2}$. This occurs at $x = \frac{2\pi}{3}$ and $x = \frac{4\pi}{3}$ in radians.
2. Determine which of these angles has a negative sine value. The sine function is negative in the third and fourth quadrants.
3. Since $\frac{2\pi}{3}$ is in the second quadrant and $\frac{4\pi}{3}$ is in the third quadrant, we choose $x = \frac{4\pi}{3}$.
Therefore, the value of $x$ is:
$ x = \frac{4\pi}{3} $
Answer 2
Ava Martin
To find $x$ where $cos(x) = -frac{1}{2}$ and $sin(x)$ is negative:
1. Note that $cos(x) = -frac{1}{2}$ at angles $x = frac{2pi}{3}$ and $x = frac{4pi}{3}$.
2. Check the sine value: $sin(x)$ is negative in the third and fourth quadrants.
3. Since $frac{4pi}{3}$ is in the third quadrant where $sin(x)$ is negative, the answer is:
$ x = frac{4pi}{3} $
Answer 3
Henry Green
Solve for $x$ where $cos(x) = -frac{1}{2}$ and $sin(x)$ is negative.
The angle $x = frac{4pi}{3}$ satisfies both conditions.
$ x = frac{4pi}{3} $
Start Using PopAi Today