Understanding Coterminal Angles | Explained with Examples and Formulas

Coterminal Angles

Coterminal angles are angles that have the same initial and terminal sides

Coterminal angles are angles that have the same initial and terminal sides. In other words, coterminal angles are angles that coincide with each other when drawn in standard position on the coordinate plane.

To understand coterminal angles, it is important to understand what an angle in standard position means. An angle in standard position is formed by a ray (called the initial side) that starts at the origin (0, 0) of a coordinate plane and another ray (called the terminal side) that rotates counterclockwise from the initial side.

Coterminal angles are obtained by adding or subtracting a multiple of 360 degrees or 2π radians to the given angle. By doing so, the terminal side is rotated by a full revolution on the coordinate plane, which means it ends up at the same location as the initial side.

For example, let’s say we have an angle of 45 degrees. We can find coterminal angles by adding or subtracting multiples of 360 degrees.

– Adding 360 degrees: 45 + 360 = 405 degrees
– Subtracting 360 degrees: 45 – 360 = -315 degrees

Both 405 degrees and -315 degrees are coterminal angles of 45 degrees because they have the same initial and terminal sides.

Coterminal angles can also be found using radians. Since there are 2π radians in a full revolution, we can add or subtract multiples of 2π radians to find coterminal angles.

For example, if we have an angle of π/4 radians (which is equivalent to 45 degrees), we can find coterminal angles by adding or subtracting multiples of 2π radians.

– Adding 2π radians: π/4 + 2π = 9π/4 radians
– Subtracting 2π radians: π/4 – 2π = -7π/4 radians

Both 9π/4 radians and -7π/4 radians are coterminal angles of π/4 radians.

It is important to note that while coterminal angles have the same initial and terminal sides, their measures can vary. For example, 45 degrees and 405 degrees are coterminal angles, but they are not the same angle since they have different measures.

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