To determine equivalent angles for the polar point (3, 310°), we'll need to consider the properties of rotation in a circle. Adding or subtracting multiples of 360° to any given angle results in an angle that is directionally equivalent but represents different rotations.
Here's how we find three points with different angles that are equivalent to (3, 310°):
1. Starting Point:
- The given polar point is (3, 310°).
2. Finding the first equivalent point:
- Add 360° to the initial angle:
[tex]\[
310° + 360° = 670°
\][/tex]
- So, the first equivalent point is (3, 670°).
3. Finding the second equivalent point:
- Add another 360° to the initial angle:
[tex]\[
310° + 2 \times 360° = 1030°
\][/tex]
- Thus, the second equivalent point is (3, 1030°).
4. For variety, we also find an equivalent point using subtraction:
- Subtract 360° from the initial angle:
[tex]\[
310° - 360° = -50°
\][/tex]
- Optionally, you can also present this point, but we already gathered three points.
Therefore, with these calculations, the three points in polar form, with angles in degrees, that are equivalent to (3, 310°) are:
1. (3, 310°)
2. (3, 670°)
3. (3, 1030°)
These points represent the same location in the polar coordinate system but with rotation angles that differ by multiples of 360°.
