Length: L = |Atⁿ + B|
Endpoint: x = L cos(t),   y = L sin(t)
The absolute value keeps every line length non-negative.

Radius: r = Atⁿ + B
Cartesian conversion: x = r cos(t),   y = r sin(t)
The radius may be negative. The angle t is measured in radians.

Function: y = kx + b
Slope (k): determines the direction and steepness of the line.
Y-intercept (b): determines where the line crosses the y-axis.

Function: y = ax² + bx + c
Condition: a ≠ 0
Vertex Form: y = a(x + b 2a )² + c − b² 4a
Axis of Symmetry: x = − b 2a
Coefficient (a): determines the opening direction and width.
Coefficient (b): helps determine the vertex and axis of symmetry.
Coefficient (c): determines the y-intercept.

Function: y = A sin(ωx + φ) + D
A: amplitude factor · ω: angular-frequency factor · φ: phase offset · D: vertical shift
Angles are measured in radians. 2π rad = 360°. The ω slider ranges from −2 to 2; at ω = 0 the function is constant.

Function: y = A cos(ωx + φ) + D
A: amplitude factor · ω: angular-frequency factor · φ: phase offset · D: vertical shift
Angles are measured in radians. 2π rad = 360°. The ω slider ranges from −2 to 2; at ω = 0 the function is constant.

Sine: y = A sin(ωx + φ) + D
Cosine: y = A cos(ωx + φ) + D
Both curves share the same A, ω, φ, and D so you can compare their shapes directly.
Angles are measured in radians. 2π rad = 360°. The ω slider ranges from −2 to 2; at ω = 0 both functions are constant.

Unit circle: x² + y² = 1
Horizontal coordinate: cos θ   ·   Vertical coordinate: sin θ
Move θ from 0° to 720° and watch the same point generate two full turns. 2π rad = 360°.