\[\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\]

\[\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\]

\[\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\]

\[\tan\theta = \frac{\sin\theta}{\cos\theta}\]

For angle \(\theta\) measured from the positive x-axis:

\[\cos\theta = x\text{-coordinate}\]

\[\sin\theta = y\text{-coordinate}\]

• Point on unit circle: \((\cos\theta, \sin\theta)\)
• Radius = 1
• Equation: \(x^2 + y^2 = 1\)

\[\sin^2\theta + \cos^2\theta = 1\]

\[1 + \tan^2\theta = \sec^2\theta\]

\[1 + \cot^2\theta = \csc^2\theta\]

\[\sec\theta = \frac{1}{\cos\theta}\]

\[\csc\theta = \frac{1}{\sin\theta}\]

\[\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}\]

\[\sin(A + B) = \sin A \cos B + \cos A \sin B\]

\[\sin(A - B) = \sin A \cos B - \cos A \sin B\]

\[\cos(A + B) = \cos A \cos B - \sin A \sin B\]

\[\cos(A - B) = \cos A \cos B + \sin A \sin B\]

\[\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\]

\[\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}\]

\[\sin(2A) = 2\sin A \cos A\]

\[\cos(2A) = \cos^2 A - \sin^2 A\]

\[\cos(2A) = 2\cos^2 A - 1\]

\[\cos(2A) = 1 - 2\sin^2 A\]

\[\tan(2A) = \frac{2\tan A}{1 - \tan^2 A}\]

\[\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\]

\[c^2 = a^2 + b^2 - 2ab\cos C\]

\[\cos C = \frac{a^2 + b^2 - c^2}{2ab}\]

\[\text{Area} = \frac{1}{2}ab\sin C\]

\[\text{Area} = \frac{1}{2}bc\sin A\]

\[\text{Area} = \frac{1}{2}ac\sin B\]

\[\cos(-\theta) = \cos\theta\]

\[\sin(-\theta) = -\sin\theta\]

\[\tan(-\theta) = -\tan\theta\]

Sine and Cosine: Period = \(2\pi\) or \(360°\)

Tangent: Period = \(\pi\) or \(180°\)

For \(y = \sin(bx)\) or \(y = \cos(bx)\): Period = \(\frac{2\pi}{|b|}\)
For \(y = \tan(bx)\): Period = \(\frac{\pi}{|b|}\)