Exploring Coterminal Angles: Understanding and Finding Coterminal Angles in Degrees and Radians

Coterminal Angles

Coterminal angles are angles that have the same initial and terminal sides and differ by a multiple of 360 degrees or 2π radians

Coterminal angles are angles that have the same initial and terminal sides and differ by a multiple of 360 degrees or 2π radians. In simpler terms, coterminal angles are angles that have the same position on the unit circle but can differ in the number of complete revolutions made.

To find coterminal angles, you can add or subtract multiples of 360 degrees or 2π radians. Here’s how you can do it:

1. Given an angle, let’s say 45 degrees, to find a positive coterminal angle, you can add multiples of 360 degrees. For example, adding 360 degrees to 45 degrees gives you 405 degrees.

2. To find a negative coterminal angle, you can subtract multiples of 360 degrees. Subtracting 360 degrees from 45 degrees gives you -315 degrees.

3. Another way to find coterminal angles is by using radians. Let’s convert the angle 45 degrees to radians. We know that 180 degrees is equal to π radians, so 45 degrees is equal to (45/180) * π radians, which simplifies to π/4 radians.

4. Now, to find coterminal angles in radians, you can add or subtract multiples of 2π radians. Adding 2π radians to π/4 radians gives you (8π/4) + (π/4) = 9π/4 radians.

5. Similarly, subtracting 2π radians from π/4 radians gives you (0π/4) – (8π/4) = -7π/4 radians.

So, for the given angle of 45 degrees, some coterminal angles in degrees are 405 degrees and -315 degrees, while coterminal angles in radians are 9π/4 radians and -7π/4 radians.

It’s important to note that coterminal angles have the same trigonometric function values, such as sine, cosine, and tangent. This concept is useful in trigonometry when working with angles that go beyond one full revolution.

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