Ch 3 extends trigonometry from acute angles to all real numbers using the unit circle. Students learn radian measure, derive compound angle formulas, study trig graphs, and solve trigonometric equations.
An angle θ in radians = arc length / radius. π radians = 180°. 1 radian ≈ 57.3°. Trigonometric functions are defined for all real numbers using the unit circle: sin θ = y-coordinate, cos θ = x-coordinate.
sin(A±B) = sinA cosB ± cosA sinB. cos(A±B) = cosA cosB ∓ sinA sinB. tan(A±B) = (tanA ± tanB)/(1 ∓ tanA tanB). Product-to-sum and sum-to-product formulas follow from these.
General solutions: sin x = sin α → x = nπ + (−1)ⁿα. cos x = cos α → x = 2nπ ± α. tan x = tan α → x = nπ + α. Where n is any integer.
Download: https://ncert.nic.in/textbook/pdf/kemh103.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. One full revolution = 2π radians = 360°. Radians are the natural unit for measuring angles in calculus.
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