Study of triangles and trigonometric functions including sine, cosine, and tangent.
Trigonometric identities are equations involving trig functions that are always true for any angle.
Pythagorean Identity:
\[ \sin^2(\theta) + \cos^2(\theta) = 1 \]
Quotient Identities:
\[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \]
Reciprocal Identities:
\[ \csc(\theta) = \frac{1}{\sin(\theta)}, \quad \sec(\theta) = \frac{1}{\cos(\theta)}, \quad \cot(\theta) = \frac{1}{\tan(\theta)} \]
They help simplify complex problems and prove relationships between different trigonometric functions.
\[\sin^2(\theta) + \cos^2(\theta) = 1\]
Using the Pythagorean identity to find \(\sin(\theta)\) if you know \(\cos(\theta)\).
Proving that \(\tan^2(\theta)+1=\sec^2(\theta)\) using identities.
Identities help you manipulate and simplify trigonometric expressions.