1. The problem is to provide the formulas for SOHCAHTOA, the sine law, and the cosine law. 2. SOHCAHTOA is a mnemonic to remember the definitions of sine, cosine, and tangent in a right triangle: - Sine: $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$ - Cosine: $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$ - Tangent: $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$ 3. The sine law relates the sides and angles of any triangle (not necessarily right-angled): $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are the lengths of the sides opposite angles $A$, $B$, and $C$ respectively. 4. The cosine law relates the lengths of sides of any triangle to the cosine of one of its angles: $$c^2 = a^2 + b^2 - 2ab \cos C$$ This formula can be rearranged to solve for any side or angle. These formulas are fundamental in trigonometry for solving triangles and finding unknown sides or angles.