Angles and Radial Measures - Video Notes

Vocabulary flashcards covering the key concepts from the angles and radians section of the video notes.

Vertex

The common point where two rays meet to form an angle.

Initial side

One ray that forms the starting side of an angle.

Terminal side

The ray that forms the ending side of an angle.

Angle

The figure formed by two rays with a common vertex; it has an initial side and a terminal side.

Counterclockwise

The positive angular direction; angles are measured in this direction, opposite of a clock's direction.

Positive vs negative angles

Angles measured counterclockwise are positive; clockwise angles are negative (indicate direction, not magnitude).

Acute angle

An angle smaller than 90 degrees.

Right angle

An angle exactly equal to 90 degrees.

Obtuse angle

An angle between 90 and 180 degrees.

Straight angle

An angle equal to 180 degrees.

Complementary angles

Two positive angles whose measures sum to 90 degrees; in right triangles the non-right angles are complementary.

Supplementary angles

Two positive angles whose measures sum to 180 degrees.

Complementary functions

Sine and cosine are related through complementary angles (e.g., sin(θ) = cos(90°−θ) in degrees; sin(θ) = cos(π/2−θ) in radians).

Radian

A non-dimensional unit for measuring angles; defined so that the arc length equals the radius. One radian is the angle subtended by an arc length equal to the circle's radius.

Degree-to-radian conversion factor

To convert degrees to radians, multiply by π/180; to convert radians to degrees, multiply by 180/π; keep answers in terms of π (don’t convert π to 3.14).

Unit circle

A circle with radius 1 used to study special angles; the unit circle focuses on these special angles.

Central angle

An angle whose vertex is at the center of a circle.

Degree-to-radian conversion examples

Examples of converting degree measures to radians: 120° → 2π/3; -310° → -31π/18; 720° → 4π; 450° → 5π/2.