## Trigonometry Maths All Formulas List

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (CSC). These six trigonometric functions in relation to a right triangle are displayed in the figure.

Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding. Problems involving angles and distances in one plane are covered in plane trigonometry. Applications to similar problems in more than one plane of three-dimensional space are considered in spherical trigonometry.

### Trigonometry All Formulas List

**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

**Cofunction Identity**

- sin(900−x)=cosx
- cos(900−x)=sinx
- tan(900−x)=cotx
- cot(900−x)=tanx
- sec(900−x)=cosecx
- cosec(900−x)=secx

**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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