What are Trig Identities? š
A **trigonometric identity** is an equation involving trigonometric functions that is true for all values where the functions are defined. Think of them as fundamental rules that let you manipulate and simplify complex trig expressions. We'll explore the three main types:
1. **Reciprocal Identities:** The basic relationships between trig functions.
2. **Quotient Identities:** How sine, cosine, and tangent relate.
3. **Pythagorean Identities:** Derived from the Pythagorean theorem on the unit circle.
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Video: The Unit Circle & Identities š¬
Watch this video to visualize where the Pythagorean identities come from.
Practice Problems
Match the expression to its simplified form using the fundamental identities.
1) What does $\sin^2\theta + \cos^2\theta$ equal?
2) Simplify: $\frac{\sin\theta}{\cos\theta}$
3) Simplify: $\frac{1}{\cos\theta}$
4) What does $\sec^2\theta - \tan^2\theta$ equal?
ā” Trig Identities Speed Quiz
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