The unit circle & radian measure

xy(1, 0)(−1, 0)(0, 1)(0, −1)0(cos θ, sin θ)sin θcos θ1θ
A unit circle has radius 1 and is centred at the origin. The point at angle θ is (cos θ, sin θ): cos θ is its distance along the x-axis and sin θ is its height.
  • Unit circle point

    Any point on the unit circle is (cos θ, sin θ).

  • Radian measure

    180° = π radians.

  • All angles are allowed

    Angles can be greater than 360° or negative.

Pythagorean identity

sin2 θ + cos2 θ = 1

Radian measure uses arc length on a unit circle (radius 1): s = rθ = θ. This is the standard unit in calculus.

Radian measure is essential for higher-level calculus.