Unit Circle Study Guide

Unit Circle

A circle with a radius of 1 and center at (0, 0), where every point on it is represented by (cos θ, sin θ).

Key Angles

Important angles to memorize for the unit circle, including their degree, radian, and coordinate values.

ASTC Rule

A mnemonic where Q1: All positive, Q2: Sin positive, Q3: Tan positive, Q4: Cos positive.

Radians to Degrees Conversion

Multiply radians by 180/π to convert to degrees.

Degrees to Radians Conversion

Multiply degrees by π/180 to convert to radians.

Negative angle interpretation

Negative angles correspond to a clockwise rotation on the unit circle.

Reference Angle

The acute angle that the terminal side of an angle makes with the x-axis.

Lowest Non-Negative Equivalent Angle

To find this, add 2π until the result is positive.

Cotangent Undefined Points

Cotangent is undefined when y = 0, which occurs at angles like 0° and 180°.

Reciprocal Trigonometric Functions

sec = 1/cos, csc = 1/sin, and cot = 1/tan.

Square Root Pattern

In the first quadrant, cosine has values √3/2, √2/2, 1/2, and sine values follow the reverse pattern.

Trick for Coordinates in Quadrants

Memorize coordinates in Q1, and reflect x or y values negative in other quadrants as necessary.