Calculating What Quadrant the Terminal Side of an Angle Can Be Found
Problems that You Should Practice
A. If the angle is less than or equal to 360° or 2pi radians go to the chart below.
Location |
Angle Measure in Radians |
||
0° or 360° |
Positive x axis. |
0 or 2pi |
|
between 0° & 90° |
Quadrant I |
between 0 & pi/2 | |
90° |
Positive y axis |
pi/2 | |
between 90° & 180° |
Quadrant II |
between pi/2 & pi | |
180° |
Negative x axis |
pi | |
between 180° & 270° |
Quadrant III |
between pi & 3pi/2 | |
270° |
Negative y axis |
3pi/2 | |
between 270° & 360° |
Quadrant IV |
between 3pi/2 & 2pi |
B. For angles that are more than 360° or 2pi radians do the following
| Degrees | Radians | |
| 1. Divide the given angle by 360. 2. Cut off the whole number part. 3. Multiply the remaining decimal part from step 2 by 360. 4. Find the quadrant for this angle. |
1. Convert the angle measure to degrees. Perform the process described to the left. |
Directions: Please state in what quadrant or on what axis the terminal side of the given angle can be found.
| 1. 78° | |
Step 1 |
|
Note that 78°<360°. This means go to the chart. We see that 0<78°<90°, therefore, 78° is in quadrant I. |
|
| 2. 8920° | |
| 8920°>360° | |
Step 1 |
|
| 8920÷360=24.78 | |
Step 2 |
|
Step 3 |
|
| 360*.78=280.8 | |
Step 4 |
|
| 280.8° is in quadrant IV |
Problems that You Should Practice
Directions: Please state in what quadrant or on what axis the terminal side of the given angle can be found.
1. 361° 2. 9032° 3. 7601°
4. 705pi rads 5. 203.75 rads 6. 9pi/2 rads
7. 22.78° 8. 450° 9. 4590°