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
Pythagorean Identities
Trig Values Table
*N.D. – Not Defined
Sum/Difference Formulas
Double Angle Identities
2θ
cos 2θ
3θ
Sum to Product of Two Angles
Product to Sum of Two Angles
Law of sines
Law of cosines
Area of Triangle
Download Trigonometric Identities PDF
Related lessons: The Pythagorean Theorem
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