Trigonometric Functions

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The word 'trigonometry' is derived from the Greek words 'trigon' (triangle) and 'metron' (measuring). It literally means 'measuring the sides of a triangle'. Originally developed to solve geometric pr…

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An angle is a measure of rotation of a given ray about its initial point. Components: (1) Initial side - the original ray, (2) Terminal side - final position after rotation, (3) Vertex - point of rota…

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If a rotation from initial side to terminal side is 1/360th of a complete revolution, the angle has a measure of one degree (1°). Subdivisions: 1° = 60 minutes (60'), 1' = 60 seconds (60''). This syst…

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Radian measure: An angle subtended at the centre by an arc of length 1 unit in a unit circle (radius = 1 unit) has a measure of 1 radian. In a circle of radius r, an arc of length l subtends an angle …

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2π radians = 360° or π radians = 180°. Conversion formulas: 1 radian = (180°/π) ≈ 57°16', 1° = (π/180) radian ≈ 0.01746 radian. Radian measure = (π/180°) × Degree measure, Degree measure = (180°/π) × …

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30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. These are the most commonly used angle conversions that should be memorized.

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For a unit circle with center at origin, if P(a,b) is any point on the circle with angle AOP = x radians, then: cos x = a (x-coordinate), sin x = b (y-coordinate). Since it's a unit circle, a² + b² = …

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Quadrantal angles are integral multiples of π/2: 0, π/2, π, 3π/2, 2π. Values: cos 0 = 1, sin 0 = 0; cos π/2 = 0, sin π/2 = 1; cos π = -1, sin π = 0; cos 3π/2 = 0, sin 3π/2 = -1; cos 2π = 1, sin 2π = 0…