T-Ratios for Angle of 30°
In ΔPMO and ΔP′MO,
OM = OM (Common)
∠PMO = ∠P′MO (Each = 90°)
PM = P′M (Construction)
∴ ΔPMO ≅ ΔP′MO
∴ ∠OPM = ∠OP′M = 60°
∴ OPP′ is an equilateral triangle
∴ OP = OP′
Let PM = a units
PP′ = PM + MP′ = 2a units
∴ OP = OP′ = PP′ = 2a units
In right triangle PMO,
OP2 = PM2 + OM2 (Pythagoras Theorem)
(2a)2 = a2 + OM2
∴ OM2 = 3a2
OM = √3a units
sin 30° = 1/2
cos 30° = √3/2
tan 30° = 1/√3
cosec 30° = 2
sec 30° = 2/√3
cot 30° = √3