All Trigonometric Formulas, Formulas For Class 11 And 12, NCERT PDF Free Download
All Trigonometric Formulas PDF Download
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 Trognometry 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
In Trigonometry, Different Types Of Problems Can Be Solved Using Trigonometry Formulas. These Problems May Include Trigonometric Ratios (Sin, Cos, Tan, Sec, Cosec And Cot), Pythagorean Identities, Product Identities, Etc. Some Formulas Including The Sign Of Ratios In Different Quadrants, Involving Co-function Identities (Shifting Angles), Sum & Difference Identities, Double Angle Identities, Half-angle Identities, Etc., Are Also Given In Brief Here.
Learning And Memorizing These Mathematics Formulas In Trigonometry Will Help The Students Of Classes 10, 11, And 12 To Score Good Marks In This Concept. They Can Find The Trigonometry Table Along With Inverse Trigonometry Formulas To Solve The Problems Based On Them.
When We Learn About Trigonometric Formulas, We Consider Them For Right-angled Triangles Only. In A Right-angled Triangle, We Have 3 Sides Namely – Hypotenuse, Opposite Side (Perpendicular), And Adjacent Side (Base). The Longest Side Is Known As The Hypotenuse, The Side Opposite To The Angle Is Perpendicular And The Side Where Both Hypotenuse And Opposite Side Rests Is The Adjacent Side.
There Are Basically 6 Ratios Used For Finding The Elements In Trigonometry. They Are Called Trigonometric Functions. The Six Trigonometric Functions Are Sine, Cosine, Secant, Cosecant, Tangent And Cotangent.
All These Are Taken From A Right-angled Triangle. When The Height And Base Side Of The Right Triangle Are Known, We Can Find Out The Sine, Cosine, Tangent, Secant, Cosecant, And Cotangent Values Using Trigonometric Formulas. The Reciprocal Trigonometric Identities Are Also Derived By Using The Trigonometric Functions.
All Trigonometric Identities Are Cyclic In Nature. They Repeat Themselves After This Periodicity Constant. This Periodicity Constant Is Different For Different Trigonometric Identities. Tan 45° = Tan 225° But This Is True For Cos 45° And Cos 225°. Refer To The Above Trigonometry Table To Verify The Values.
Here We Provide A List Of All Trigonometry Formulas For The Students. These Formulas Are Helpful For The Students In Solving Problems Based On These Formulas Or Any Trigonometric Application. Along With These, Trigonometric Identities Help Us To Derive The Trigonometric Formulas If They Appear In The Examination.
We Also Provided The Basic Trigonometric Table PDF That Gives The Relation Of All Trigonometric Functions Along With Their Standard Values. These Trigonometric Formulae Are Helpful In Determining The Domain, Range, And Value Of A Compound Trigonometric Function. Students Can Refer To The Formulas Provided Below Or Download The Trigonometric Formulas PDF Provided Above.