Trigonometry: Angles and Unit Circle Vocabulary

Vocabulary flashcards covering standard position, reference angles, unit circle concepts, trig definitions, reciprocal identities, and special right triangles.

Standard Position

An angle with the vertex at the origin, initial side on the positive x-axis, and a terminal side determined by the angle.

Initial Side

The ray along the positive x-axis from the origin in standard position.

Terminal Side

The ray where the angle ends after rotation from the initial side.

Radians

A measure of angle where 2π radians = 360°, and π radians = 180°; arc length is proportional to the angle measure.

Degrees

A measure of angle where 360° = 2π radians; the circle is divided into 360 equal parts.

Reference Angle (θ′)

The acute angle formed between the terminal side of θ and the x-axis; used to compute trig values regardless of quadrant.

Reference Angle in Quadrant II

If θ is in Quadrant II, the reference angle θ′ = 180° − θ (or π − θ).

Reference Angle in Quadrant III

If θ is in Quadrant III, the reference angle θ′ = θ − 180° (or θ − π).

Reference Angle in Quadrant IV

If θ is in Quadrant IV, the reference angle θ′ = 360° − θ (or 2π − θ).

Coterminal Angles

Angles that share the same terminal side; their measures differ by full rotations (360° or 2π).

P = (x, y) and r

A point P with coordinates (x, y); r is the distance from the origin to P, r = √(x^2 + y^2).

Unit Circle

Circle of radius 1 centered at the origin; x^2 + y^2 = 1; cos θ = x, sin θ = y.

Cosine, Sine, Tangent (ratios)

cos θ = adjacent/hypotenuse; sin θ = opposite/hypotenuse; tan θ = opposite/adjacent.

Reciprocal Trigonometric Identities

sec θ = hypotenuse/adjacent = r/x; csc θ = hypotenuse/opposite = r/y; cot θ = adjacent/opposite = x/y.

Cosine/Sine/Tangent in terms of x, y, r

cos θ = x/r; sin θ = y/r; tan θ = y/x (x ≠ 0).

Unit Circle Coordinates for Standard Angles

On the unit circle, θ = 0°: P = (1,0); θ = 90°: P = (0,1); θ = 180°: P = (−1,0); θ = 270°: P = (0,−1).

Special Right Triangles

30-60-90 triangle with sides in ratio 1:√3:2; 45-45-90 triangle with sides in ratio 1:1:√2; used for exact trig values.

30-60-90 Values

For 30°: sin = 1/2, cos = √3/2, tan = 1/√3; for 60°: sin = √3/2, cos = 1/2, tan = √3.

45-45-90 Values

For 45°: sin = cos = √2/2, tan = 1.

Special Angles on the Unit Circle

Angles with axis coordinates: 0°, 90°, 180°, 270° and their corresponding P points on the unit circle.