Calculating Coterminal Angles in Radians: A Comprehensive Guide

TLDR; Determining coterminal angles in radians involves adding or subtracting multiples of 2/PI radians to a given angle. This process helps identify positive and negative coterminal angles with the same terminal side.

📐 Sketching the Angle

The angle in radians is sketched in a standard position, with the initial side and terminal side identified.

The angle of PI/3 radians is approximately equivalent to 60 degrees.

To determine another coterminal angle with the same terminal side, multiples of 2/PI radians are added or subtracted from the given angle in radians.

🔢 Calculating Coterminal Angles

To find another positive coterminal angle to PI/3 radians, 2/PI is added to the angle.

The resulting angle is calculated as 7PI/3 radians, representing the same terminal side as the initial angle.

For a negative coterminal angle, 2/PI radians are subtracted from the given angle, resulting in -5PI/3 radians.

🔄 General Rule for Coterminal Angles

The general rule for determining coterminal angles in radians involves adding or subtracting multiples of 2/PI x (K), where (K) is an integer.

Adding multiples of 2/PI results in positive coterminal angles, while subtracting multiples of 2/PI yields negative coterminal angles.

🔄 Handling Negative Angles

When dealing with negative angles in radians, the process of adding or subtracting multiples of 2/PI radians is still applied.

For example, to find a negative coterminal angle to -4PI/5 radians, multiples of 2/PI are added or subtracted accordingly.

📏 Finding Additional Coterminal Angles

By adding 10PI/5 radians to the given angle -4PI/5, the result is 6PI/5 radians, representing another negative coterminal angle.

Subtracting 10PI/5 radians from the given angle yields -14PI/5 radians, indicating another negative coterminal angle.

Frequently asked questions

How do you determine coterminal angles in radians?

Coterminal angles in radians are determined by adding or subtracting multiples of 2/PI radians to a given angle, which helps identify positive and negative coterminal angles with the same terminal side.

What is the general rule for coterminal angles in radians?

The general rule involves adding or subtracting multiples of 2/PI x (K), where (K) is an integer. Adding multiples results in positive coterminal angles, while subtracting multiples yields negative coterminal angles.

How are coterminal angles calculated?

To find another positive coterminal angle, add 2/PI to the given angle; for negative coterminal angle, subtract 2/PI from the given angle. The resulting angles share the same terminal side as the initial angle.

What process is used to handle negative angles in radians?

When dealing with negative angles in radians, the process of adding or subtracting multiples of 2/PI radians is still applied to find negative coterminal angles.