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

$\pi \text{ radians} = 180^{\circ}$

$P = (\cos(\theta), \sin(\theta))$

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$

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

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

$x^2 + y^2 = r^2$, and since r=1, $x^2 + y^2 = 1$

$\theta + 2\pi k$, where k is an integer.

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

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

The y-coordinates of points on the unit circle correspond to the y-values of the sine graph, and the x-coordinates correspond to the y-values of the cosine graph, as the angle increases.

The period (2π) represents one full revolution around the unit circle.

The amplitude represents the maximum distance from the x-axis, which corresponds to the radius of the unit circle (1 in the standard case).

A phase shift represents a horizontal translation, corresponding to a different starting point on the unit circle.

By observing the signs of the y-values (sine) and x-values (cosine), you can determine the quadrant based on the ASTC rule.

The integral of sin(x) is -cos(x) + C, which represents the area under the sin(x) curve. The constant C shifts the cosine graph vertically.

The integral of cos(x) is sin(x) + C, which represents the area under the cos(x) curve. The constant C shifts the sine graph vertically.

The steepness is related to how quickly the y or x coordinate changes as you move along the unit circle, which is greatest near 0 and π for cosine and π/2 and 3π/2 for sine.

A circle with a radius of 1, centered at the origin (0,0).

An angle that starts from the positive x-axis and goes counterclockwise.

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

A line from the origin at a given angle that intersects the unit circle.

The y-coordinate of the point where the terminal ray intersects the unit circle.

The x-coordinate of the point where the terminal ray intersects the unit circle.

The ratio of the y-coordinate to the x-coordinate (sin θ / cos θ) of the point where the terminal ray intersects the unit circle.

Angles greater than 180° but less than 360°.

2π radians.

A mnemonic to remember which trig functions are positive in each quadrant: All, Sine, Tangent, Cosine.