In trigonometry, various formulas help solve problems involving trigonometric ratios (sin, cos, tan, sec, cosec, and cot), Pythagorean identities, and more. These formulas are essential for students in classes 10, 11, and 12 to score well in exams. Here is a simplified guide to the key trigonometric formulas.
Basic Trigonometric Function Formulas
In a rightangled triangle:
 Hypotenuse: The longest side
 Opposite side (Perpendicular): The side opposite to the angle
 Adjacent side (Base): The side next to the angle
The six trigonometric functions are:
Reciprocal Identities
These identities express trigonometric functions in terms of their reciprocals:
Trigonometry Table













Periodicity Identities (in Radians)
These identities shift angles by Ï€/2, Ï€, 2Ï€, etc.:
Cofunction Identities (in Degrees)
These identities relate trigonometric functions of complementary angles:
Sum & Difference Identities
Double Angle Identities
Triple Angle Identities
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Half Angle Identities
Inverse Trigonometry Formulas
Trigonometry Formulas Major Systems
Trigonometric formulas are divided into two main categories:
 Trigonometric Identities: These are true for all values of the variables.
 Trigonometric Ratios: These relate the angles to the sides of a rightangled triangle.
These formulas are crucial for solving problems in trigonometry and understanding various applications in mathematics.
FAQs
Double angle identities express trigonometric functions of double angles:
Sum and difference identities are used to find the sine and cosine of the sum or difference of two angles:
Periodicity identities allow shifting angles by , etc.:
Reciprocal identities relate trigonometric functions to their reciprocals:
The basic trigonometric functions are:
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