# Trig Identities

# Trig Identities

- The trigonometric identities are mathematical equations that relate the trigonometric functions (sin, cos, tan) to one another.
- There are many identities in trigonometry, but for revision, we are focusing on the primary ones: Pythagorean identities, Quotient identities, Co-Function identities, and Even-Odd identities.
**Pythagorean identities**form the basis of trigonometry and are based on the Pythagorean theorem. These include`sin²θ + cos²θ = 1`

,`tan²θ + 1 = sec²θ`

, and`cot²θ + 1 = csc²θ`

.**Quotient identities**express the functions in terms of each other.`tan(θ) = sin(θ)/cos(θ)`

and`cot(θ) = cos(θ)/sin(θ)`

.**Co-Function identities**describe the relationship between the sine and cosine of complementary angles.`sin(90° – θ) = cos(θ)`

and`cos(90° – θ) = sin(θ)`

**Even-Odd identities**pertain to the symmetry of the sin, cos, and tan functions.`sin(–θ) = -sin(θ)`

,`cos(–θ) = cos(θ)`

, and`tan(–θ) = -tan(θ)`

.- The key to mastering trig identities is practise. Work through several examples and apply each identity correctly.
- Remember, these identities will help later when solving trig equations or simplifying expressions.