Determine the quadrant in which the terminal side of the given angle lies.
230°
To determine the quadrant in which the terminal side of the angle 230° lies, we need to understand the relationship between angles and quadrants on the coordinate plane.
Firstly, remember that a full circle is 360°. Therefore, an angle of 230° is more than half of a circle but less than a full circle.
To find the quadrant, we can start by examining the quadrants in the coordinate plane:
- Quadrant I: angles between 0° and 90°
- Quadrant II: angles between 90° and 180°
- Quadrant III: angles between 180° and 270°
- Quadrant IV: angles between 270° and 360°
Since 230° is greater than 180° but less than 270°, the terminal side of the angle 230° lies in Quadrant III.
To determine the quadrant in which the terminal side of the angle 230° lies, follow these steps:
1. Subtract 360° from the given angle until the result is between 0° and 360°.
230° - 360° = -130°
2. If the result is negative, add 360° to it to find the equivalent positive angle.
-130° + 360° = 230°
3. The terminal side lies in the same quadrant as the equivalent positive angle. In this case, the terminal side of the angle 230° lies in the third quadrant.
Therefore, the quadrant in which the terminal side of the angle 230° lies is the third quadrant.
well it is more than 180 and less than 270
so
I claim it is in the third