Unit Circle and Radians

Any angle, from a point (x, y) at distance r

Distance

r = \sqrt{x^{2} + y^{2}}

Sine and cosine

\sin θ = \frac{y}{r} \cos θ = \frac{x}{r}

Tangent

\tan θ = \frac{y}{x}

x ≠ 0

Reciprocals

\csc θ = \frac{r}{y} \sec θ = \frac{r}{x} \cot θ = \frac{x}{y}

Degrees to radians

radians = degrees \times \frac{π}{180^{\circ}}

Radians to degrees

degrees = radians \times \frac{180^{\circ}}{π}

Arc length

s = r θ

θ in radians

Sector area

A = \frac{1}{2} r^{2} θ = \frac{1}{2} r s

Segment area

A = \frac{1}{2} r^{2} (θ - \sin θ)

Angular speed

ω = \frac{θ}{t}

Linear speed

v = \frac{s}{t} = r ω

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