Vertex at the origin, initial ray along the positive x-axis.

Angles sharing the same terminal ray, differing by multiples of 360° (or 2π radians).

Angle measure based on the arc length subtended on a circle; ratio of arc length to radius.

Ratio of the y-coordinate of a point on the unit circle to the radius: sin(θ) = y/r.

Ratio of the x-coordinate of a point on the unit circle to the radius: cos(θ) = x/r.

Slope of the terminal ray; ratio of the y-coordinate to the x-coordinate: tan(θ) = y/x.

tan(θ) = sin(θ) / cos(θ)

[-1, 1]

[-1, 1]

All real numbers.

Sine starts at 0 at x=0, cosine starts at 1 at x=0 | Sine is an odd function, cosine is an even function

Sine is a wave that passes through the origin, cosine is a wave that starts at its maximum value | Sine and cosine have the same period and amplitude but are shifted horizontally by π/2.

Tangent has a period of π, sine/cosine have a period of 2π | Tangent has vertical asymptotes, sine/cosine are continuous.

Sine and cosine have a range of [-1, 1] | Tangent has a range of all real numbers.

Sine increases from 0 to 1 | Cosine decreases from 1 to 0

Sine is zero at multiples of π | Cosine is zero at odd multiples of π/2

The derivative of sine is cosine | The derivative of cosine is -sine

Positive angles are measured counterclockwise | Negative angles are measured clockwise

Radians are based on the radius of a circle | Degrees are an arbitrary division of a circle into 360 parts

y = sin(-x) is a reflection of y = sin(x) across the x-axis | sin(x) is an odd function, so sin(-x) = -sin(x)

$\sin(\theta) = \frac{y}{r}$

$\cos(\theta) = \frac{x}{r}$

$\tan(\theta) = \frac{y}{x}$

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

$\text{radians} = \text{degrees} \times \frac{\pi}{180}$

$\text{degrees} = \text{radians} \times \frac{180}{\pi}$

$\sin(2x) = 2\sin(x)\cos(x)$

$\sin^2(\theta) + \cos^2(\theta) = 1$

$2\pi$

$\pi$