trig identities

Trigonometric Identities

A Trigonometric identity or trig identity is an identity that contains the trigonometric functions sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), or cosecant(csc). Trigonometric identities can use to:

  • Simplify trigonometric expressions.
  • Solve trigonometric equations.
  • Prove that one trigonometric expression is equivalent to another so that we can replace the first expression by the second expression. The following expression can give us new insights into some applications that the first one doesn’t show.
  • Quotient Identities
  • Pythagorean Identities
  • Trig Values Table
  • Sum/Difference Formulas
  • Double Angle Identities
  • Sum to Product of Two Angles
  • Product to Sum of Two Angles
  • Law of sines
  • Law of cosines
  • Area of Triangle

How Many Trigonometric Identities Available?

There is an infinite number of trig identities. Only a number of are useful, the rest generally ending up as problems and exercises for college students to unravel.

Basic trigonometric identities fall into four groups:

  • Reciprocals
  • Ratios
  • Products
  • Pythagorean Theorem

Quotient Identities

quotient identities 1
quotient identities 2

Pythagorean Identities

Pythagorean Identities

Trig Values Table

Trig Values Table

*N.D. – Not Defined

Sum/Difference Formulas

Sum Difference Formulas 1
Sum Difference Formulas 2

Double Angle Identities

2θ

Double Angle Identities 2 theta

cos 2θ

Double Angle Identities cos 2 theta

3θ

Double Angle Identities 3 theta

Sum to Product of Two Angles

Sum to Product of Two Angles

Product to Sum of Two Angles

Product to Sum of Two Angles
Product to Sum of Two Angles 2
law of sines and cosines

Law of sines

Law of sines

Law of cosines

Law of cosines

Area of Triangle

Area of Triangle

Download Trigonometric Identities PDF

Related lessons: The Pythagorean Theorem

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