Determining Coterminal Angles to 68 Degrees

TLDR; Determining positive and negative coterminal angles to 68 degrees involves rotating clockwise and counterclockwise, adding or subtracting 360 degrees multiples, and changing the value of K.

💡 Definition of Coterminal Angles

Coterminal angles share the same terminal side when sketched in standard position.

To determine coterminal angles to 68 degrees, the initial side is rotated counterclockwise, providing an infinite number of coterminal angles.

Another positive coterminal angle to 68 degrees can be obtained by rotating all the way around counterclockwise and then rotating another 68 degrees counterclockwise, resulting in 428 degrees.

🔄 Finding Negative Coterminal Angle

To find a negative coterminal angle to 68 degrees, start with the same initial side and rotate clockwise until reaching the same terminal side.

By rotating clockwise from 68 degrees to -180 degrees and then to -270 degrees, the angle formed by the positive y-axis and the terminal side would be 22 degrees.

Continuing to rotate another 22 degrees clockwise gives the negative coterminal angle of -292 degrees.

📐 Writing Down the Coterminal Angles

The obtained coterminal angles are 428 degrees and -292 degrees.

It is highlighted that sketching is not necessary to determine coterminal angles to 68 degrees.

Any coterminal angle to 68 degrees would be 68 degrees plus or minus multiples of 360 degrees, representing additional revolutions around the circle.