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

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

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

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

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

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

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

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

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

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

The unit circle provides a visual representation of trigonometric functions, where the x and y coordinates of points on the circle correspond to cosine and sine values of angles, respectively.

Locate the angle on the unit circle. The x-coordinate of the point is the cosine of the angle, and the y-coordinate is the sine of the angle.

It simplifies trigonometric calculations and directly relates angles to trigonometric values without needing to account for scaling.

Positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise.

Use the ASTC rule: All functions are positive in Quadrant I, Sine is positive in Quadrant II, Tangent is positive in Quadrant III, and Cosine is positive in Quadrant IV.

Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by multiples of 2π radians or 360 degrees.

Regardless of the size of the triangle, the ratios of sides for a given angle remain constant, as defined by the unit circle.

The cyclical nature of the unit circle illustrates the periodic behavior of sine and cosine functions, repeating every 2π radians.

Locate the y-coordinate for sine or x-coordinate for cosine on the unit circle and identify the corresponding angle(s).

Sine of an angle is equal to the cosine of its complement, and vice versa (e.g., sin(θ) = cos(90° - θ)).

Sine: y-coordinate on the unit circle, odd function | Cosine: x-coordinate on the unit circle, even function

Positive angles: Measured counterclockwise | Negative angles: Measured clockwise

Radians: Based on the radius of the circle, dimensionless | Degrees: Arbitrary division of a circle into 360 parts

sin(0) = 0 | cos(0) = 1

sin(π/2) = 1 | cos(π/2) = 0

Sine: [-1, 1] | Cosine: [-1, 1]

y = sin(x): Starts at (0, 0), odd function | y = cos(x): Starts at (0, 1), even function

Derivative of sin(x): cos(x) | Derivative of cos(x): -sin(x)

Integral of sin(x): -cos(x) + C | Integral of cos(x): sin(x) + C

Sine: Opposite/Hypotenuse | Cosine: Adjacent/Hypotenuse