What is Trigonometry?

• Trigonometry (from Greek trigōnon, triangle and metron, measure) is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine.

Trigonometric Ratios of acute Angles 📐

• sinΘ = Perpendicular / Hypotenuse
• cosΘ = Base / Hypotenuse
• tanΘ = Perpendicular / Base
• secΘ = 1 / cosΘ
• cosecΘ = 1 / sinΘ
• cotΘ = 1 / tanΘ

Fundamental Trigonometric Identities

• sin²Θ + cos²Θ = 1
• 1 - cos²Θ = sin²Θ
• 1 - sin²Θ = cos²Θ
• 1 + tan²Θ = sec²Θ
• sec²Θ - 1 = tan²Θ
• sec²Θ - tan²Θ = 1
• 1 + cot²Θ = cosec²Θ
• cosec²Θ - 1 = cot²Θ
• cosec²Θ - cot²Θ = 1

Sign of Trigonometric Functions in Different Quadrants

Trigonometric Functions of Compound Angles

• sin(A+B) = sinAcosB + cosAsinB
• sin(A-B) = sinAcosB - cosAsinB
• cos(A+B) = cosAcosB + sinAsinB
• cos(A-B) = cosAcosB - sinAsinB
• tan(A+B) = tanA + tanB / 1 - tanAtanB
• tan(A-B) = tanA - tanB / 1 + tanAtanB
• cot(A+B) = cotAcotB - 1 / cotA + cotB
• cot(A-B) = cotAcotB + 1 / cotB - cotA

Transformation Formulae

• 2sinAcosB = sin(A+B) + sin(A-B)
• 2cosAsinB = sin(A+B) - sin(A-B)
• 2cosAcosB = cos(A+B) + cos(A-B)
• 2sinAsinB = cos(A-B) - cos(A+B)
• sinC + sinD = [2sin(C+D)/2].[sin(C-D)/2]
• sinC - sinD = [2cos(C+D)/2].[sin(C-D)/2]
• cosC + + cosD = [2cos(C+D)/2].[cos(C-D)/2]
• cosC + + cosD = -[2sin(C+D)/2].[sin(C-D)/2]