how to find which angle lies in which quadrant
ex: 7pi/6 3pi/2 or any one
0 - pi/2 quad 1
pi/2 to pi quad 2
pi to 3 pi/2 guad 3
3 pi/2 to 2 pi quad 4
quadrant one goes from zero to PI/2
quadrant two goes from PI/2 to PI
and so forth.
So can you determine angles <, >, or =? That answers the question.
For instance: 7PI/6 is greater than PI, but less than 3PI/2, so it is in quadrant III.
To determine which quadrant an angle lies in, you need to understand the unit circle and the concept of positive and negative angles.
The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is divided into four quadrants:
- Quadrant I is the top right quadrant, where both the x-coordinate and y-coordinate are positive.
- Quadrant II is the top left quadrant, where the x-coordinate is negative and the y-coordinate is positive.
- Quadrant III is the bottom left quadrant, where both the x-coordinate and y-coordinate are negative.
- Quadrant IV is the bottom right quadrant, where the x-coordinate is positive and the y-coordinate is negative.
Now, let's say you have an angle in radians, such as 7π/6 or 3π/2. Here's how you can determine which quadrant it lies in:
1. Convert the angle to degrees (if it's not already in degrees) by multiplying it by the conversion factor 180/π.
For example, if the angle is 7π/6:
Angle in degrees = (7π/6) * (180/π) = 210 degrees
2. Determine the quadrant based on the angle in degrees:
- If the angle is between 0 and 90 degrees, it lies in Quadrant I.
- If the angle is between 90 and 180 degrees, it lies in Quadrant II.
- If the angle is between 180 and 270 degrees, it lies in Quadrant III.
- If the angle is between 270 and 360 degrees, it lies in Quadrant IV.
For example, if the angle is 210 degrees, it lies in Quadrant III.
Keep in mind that angles in radians are often given in terms of π, so it's helpful to be familiar with the common radian measures and their corresponding degrees to determine the quadrant.