Part 2/6:
To start, we need to visualize this angle. The angle ( \frac{2\pi}{3} ) radians is located in the second quadrant, as it's greater than ( \frac{\pi}{2} ) (90 degrees) and less than ( \pi ) (180 degrees). We can plot this on a coordinate plane, where:
The x-axis represents the cosine values,
The y-axis represents the sine values.
Reference Angle
The reference angle ( \theta_r ) can be determined by subtracting the given angle from ( \pi ):
[
\theta_r = \pi - \frac{2\pi}{3} = \frac{\pi}{3}
]
This reference angle makes it easy to find the sine, cosine, and tangent values since ( \frac{\pi}{3} ) corresponds to well-known exact ratios.
Trig Ratios for π/3
Using knowledge from previous studies:
- ( \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} )