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.

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

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

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

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

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

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

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

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

$2\pi$

$\pi$

The derivative, cos(x), represents the slope of the sine function. Where sine increases, cosine is positive; where sine decreases, cosine is negative; where sine has a max/min, cosine is zero.

The derivative, -sin(x), represents the slope of the cosine function. Where cosine increases, -sine is positive; where cosine decreases, -sine is negative; where cosine has a max/min, -sine is zero.

The derivative, sec²(x), is always positive, indicating that the tangent function is always increasing (except where it's undefined).

The amplitude determines the maximum and minimum values of the function. A larger amplitude stretches the graph vertically.

The period determines how often the function repeats. A shorter period compresses the graph horizontally, while a longer period stretches it.

A vertical shift indicates a change in the midline of the function. The entire graph is shifted up or down.

A horizontal shift (phase shift) indicates a change in the starting point of the function. The entire graph is shifted left or right.

The period is the distance along the x-axis required for the function to complete one full cycle.

The amplitude is half the distance between the maximum and minimum values of the function.

The graph of sin(2x) is a horizontal compression of sin(x) by a factor of 2, meaning it oscillates twice as fast.