7 Fundamental Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables involved. These identities are essential tools in mathematics, physics, and engineering. Here, we focus on 7 fundamental trigonometric identities that form the basis of trigonometry.
1. Pythagorean Identity
- sin2(θ) + cos2(θ) = 1
This is the most fundamental Pythagorean identity, derived from the Pythagorean theorem. From this, two additional Pythagorean identities can be derived, but this is the primary identity.
2. and 3. Quotient Identities
- tan(θ) = sin(θ) / cos(θ)
- cot(θ) = cos(θ) / sin(θ)
These identities define the tangent and cotangent functions in terms of sine and cosine.
4., 5., 6., and 7. Reciprocal Identities
- csc(θ) = 1 / sin(θ)
- sec(θ) = 1 / cos(θ)
- cot(θ) = 1 / tan(θ)
- tan(θ) = 1 / cot(θ)
These identities define the reciprocal trigonometric functions: cosecant, secant, and cotangent, along with the reciprocal relationship between tangent and cotangent.
These 7 fundamental identities are crucial for simplifying trigonometric expressions, solving equations, and understanding the relationships between trigonometric functions. They form the foundation for more advanced trigonometric concepts.
Further Resources
For more detailed explanations and examples, explore these resources on trigonometric identities from www.pakmath.com: