1. The problem is to understand the basics of trigonometry, which deals with the relationships between the angles and sides of triangles. 2. The fundamental formulas in trigonometry are the definitions of sine, cosine, and tangent for a right triangle: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. Important rules include the Pythagorean identity: $$\sin^2(\theta) + \cos^2(\theta) = 1$$ 4. To apply these, identify the angle and the sides relative to it, then use the appropriate ratio. 5. For example, if a right triangle has an angle $\theta$ and the opposite side length is 3 and the hypotenuse is 5, then: $$\sin(\theta) = \frac{3}{5} = 0.6$$ 6. This means the sine of angle $\theta$ is 0.6. 7. Trigonometry also extends to non-right triangles using laws such as the Law of Sines and Law of Cosines, but the basics start with right triangles. 8. Understanding these basics allows solving for unknown sides or angles in right triangles.