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Trigonometry Formulas List

Here we have shared the Basic to Advance Formulas List in Trigonometry.

Basic Trigonometry Formulas

• sin θ = Opposite Side/Hypotenuse
• cos θ = Adjacent Side/Hypotenuse
• tan θ = Opposite Side/Adjacent Side
• sec θ = Hypotenuse/Adjacent Side
• cosec θ = Hypotenuse/Opposite Side
• cot θ = Adjacent Side/Opposite Side

Periodic Identity of Trigonometric Angles

• sin(π2–A)=cosA  & cos(π2–A)=sinA
• sin(π2+A)=cosA & cos(π2+A)=–sinA
• sin(3π)2–A)=–cosA & cos(3π2–A)=–sinA
• sin(3π2+A)=–cosA & cos(3π2+A)=sinA
• sin(π–A)=sinA & cos(π–A)=–cosA
• sin(π+A)=–sinA & cos(π+A)=–cosA
• sin(2π–A)=–sinA & cos(2π–A)=cosA
• sin(2π+A)=sinAcos(2π+A)=cosA

Sum and Difference Trigonometric Formula

• sin(x+y)=sin(x)cos(y)+cos(x)sin(y)
• cos(x+y)=cos(x)cos(y)–sin(x)sin(y)
• tan(x+y)=(tanx+tany)(1−tanx∙tany)
• sin(x–y)=sin(x)cos(y)–cos(x)sin(y)
• cos(x–y)=cos(x)cos(y)+sin(x)sin(y)
• tan(x−y)=(tanx–tany)(1+tanx∙tany)

Double Angle Formula

• sin(2x)=2sin(x)∙cos(x)=2tanx(1+tan2x)
• cos(2x)=cos2(x)–sin2(x)=(1−tan2x)(1+tan2x)
• cos(2x)=2cos2(x)−1=1–2sin2(x)
• tan(2x)=2tan(x)1−tan2(x)
• sec(2x)=sec2x(2−sec2x)
• csc(2x)=(secx.cscx)2

Inverse Trigonometric Function

• sin−1(–x)=–sin−1x
• cos−1(–x)=π–cos−1x
• tan−1(–x)=–tan−1x
• cosec−1(–x)=–cosec−1x
• sec−1(–x)=π–sec−1x
• cot−1(–x)=π–cot−1x

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