Master Trig Visuals

Unit Circle (special angles, ASTC)

Sine = y, Cosine = x, Tangent = y/x

Reference Triangle

Right triangle with sides x = r·cosθ, y = r·sinθ, hypotenuse r. Toggle r and θ.

Unit Circle → Sine & Cosine (projection)

sine cosine (dashed)

Trig Function Graphs

Inverse Trig Graphs (principal branches)

Transform Sandbox: y = A·sin(Bx − C) + D

Period = 2π, Midline = y = 0, Phase shift = 0

Degree ↔ Radian Ring

Hover/tap to see matching degree & radian labels.

Special Angles (degrees ↔ radians ↔ values)

Identity Map

Pythagorean

  • sin²θ + cos²θ = 1
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = csc²θ

Reciprocal

  • secθ = 1 / cosθ, cscθ = 1 / sinθ, cotθ = 1 / tanθ

Quotient

  • tanθ = sinθ / cosθ, cotθ = cosθ / sinθ

Cofunction (complements)

  • sin(π/2−θ)=cosθ, cos(π/2−θ)=sinθ
  • tan(π/2−θ)=cotθ, sec(π/2−θ)=cscθ

Sum/Difference

  • sin(a±b)=sin a cos b ± cos a sin b
  • cos(a±b)=cos a cos b ∓ sin a sin b
  • tan(a±b)= (tan a ± tan b)/(1 ∓ tan a tan b)

Double / Half

  • sin 2θ=2 sinθ cosθ, cos 2θ=cos²θ−sin²θ=1−2 sin²θ=2 cos²θ−1
  • tan 2θ=2 tanθ/(1−tan²θ)

ASTC rule: All (Q1) — Sine (Q2) — Tangent (Q3) — Cosine (Q4).