1. The most common angle formulas are for right triangles and trigonometric identities. 2. In a right triangle, the sum of angles is $180^\circ$ and one angle is $90^\circ$. So, if one acute angle is $\theta$, the other acute angle is $90^\circ - \theta$. 3. Basic trigonometric ratios for an angle $\theta$ are: - Sine: $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ - Cosine: $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ - Tangent: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ 4. Pythagorean identity: $$\sin^2 \theta + \cos^2 \theta = 1$$ 5. Angle sum and difference formulas: $$\sin (a \pm b) = \sin a \cos b \pm \cos a \sin b$$ $$\cos (a \pm b) = \cos a \cos b \mp \sin a \sin b$$ 6. Double angle formulas: $$\sin 2\theta = 2 \sin \theta \cos \theta$$ $$\cos 2\theta = \cos^2 \theta - \sin^2 \theta$$ 7. Law of sines for any triangle: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 8. Law of cosines for any triangle: $$c^2 = a^2 + b^2 - 2ab \cos C$$ These formulas help calculate unknown angles or sides depending on the given information in triangles.