Coterminal Angles
Coterminal angles are angles that have the same initial side and the same terminal side in the coordinate plane
Coterminal angles are angles that have the same initial side and the same terminal side in the coordinate plane. In other words, coterminal angles are angles that differ by a multiple of 360 degrees or 2π radians.
To find coterminal angles, you can add or subtract multiple turns of 360 degrees or 2π radians to the given angle.
For example, let’s say we have an angle of 45 degrees. To find a positive coterminal angle, we can add 360 degrees to 45 degrees:
45 degrees + 360 degrees = 405 degrees
So, 405 degrees is a positive coterminal angle with 45 degrees.
Similarly, we can find a negative coterminal angle by subtracting 360 degrees from 45 degrees:
45 degrees – 360 degrees = -315 degrees
Therefore, -315 degrees is a negative coterminal angle with 45 degrees.
In radians, we can use the same concept. Let’s say we have an angle of π/3 radians. To find a positive coterminal angle, we can add 2π radians to π/3 radians:
π/3 radians + 2π radians = 7π/3 radians
So, 7π/3 radians is a positive coterminal angle with π/3 radians.
To find a negative coterminal angle, we can subtract 2π radians from π/3 radians:
π/3 radians – 2π radians = -5π/3 radians
Hence, -5π/3 radians is a negative coterminal angle with π/3 radians.
In summary, coterminal angles are angles that have the same initial and terminal sides. They can be found by adding or subtracting multiples of 360 degrees or 2π radians to a given angle.
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