how to find coterminal angles

Question

Coterminal angles are angles that share the same initial and terminal sides. In other words, they rotate the same amount around a central point. There are infinitely many coterminal angles for any given angle.

Here's how to find coterminal angles:

Answer 1

Degrees:

1. Add or subtract multiples of 360° to the original angle.

Adding 360° rotates the angle a full circle and lands you in the same spot. Subtracting 360° does the same thing in the opposite direction.

• Example: Find a coterminal angle of 45°.
  • Add 360°: 45° + 360° = 405°
  • Subtract 360°: 45° - 360° = -315° (negative angles are also valid)

Radians:

1. Add or subtract multiples of 2π to the original angle.

Similar to degrees, adding 2π rotates the angle a full circle. Subtracting 2π achieves the same effect in the opposite direction.

• Example: Find a coterminal angle of π/3 radians.
  • Add 2π: π/3 + 2π = (7π)/3
  • Subtract 2π: π/3 - 2π = -5π/3 (negative angles are also valid)

Key points to remember:

• You can find multiple coterminal angles by adding or subtracting multiples of 360° (or 2π) as many times as needed.
• Coterminal angles have the same trigonometric values (sine, cosine, tangent).