Topic 03

Trigonometry

Angles, triangles, and waves. Master sine, cosine, and tangent — and discover how they connect triangles to the world of periodic functions.

Visual Reference
Key Diagrams
Unit Circle
(cosθ, sinθ) sinθ cosθ θ x y radius = 1
Sine & Cosine Waves
1 -1 T = 2π sin(x) cos(x)
SOH CAH TOA
adjacent opposite hypotenuse θ SOH: sin = opp/hyp CAH: cos = adj/hyp TOA: tan = opp/adj
Reference
Core Formulas
Pythagorean Identity
sin²θ + cos²θ = 1
The most fundamental trig identity — always true for any angle θ.
SOH CAH TOA
sin = opp/hyp · cos = adj/hyp
tan = opp/adj. Memorize this — it's the foundation of right triangle trig.
Law of Sines
a/sinA = b/sinB = c/sinC
Relates sides and opposite angles in any triangle.
Law of Cosines
c² = a² + b² − 2ab·cosC
Generalizes the Pythagorean theorem to any triangle.
Double Angle
sin = 2sinθcosθ
cos2θ = cos²θ − sin²θ = 1 − 2sin²θ.
Reciprocal Identities
csc = 1/sin · sec = 1/cos
cot = 1/tan = cos/sin. These are the reciprocal trig functions.
Practice
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