1. Let's start with the basics of trigonometry. Trigonometry studies the relationships between the angles and sides of triangles, especially right triangles. 2. The primary functions are sine ($\sin$), cosine ($\cos$), and tangent ($\tan$). For an angle $\theta$ in 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. Also, the tangent can be expressed as: $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$ 5. Let's solve an example: Find $\sin(30^\circ)$, $\cos(30^\circ)$, and $\tan(30^\circ)$. 6. Using known values: $$\sin(30^\circ) = \frac{1}{2}, \quad \cos(30^\circ) = \frac{\sqrt{3}}{2}$$ 7. Then, $$\tan(30^\circ) = \frac{\sin(30^\circ)}{\cos(30^\circ)} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ 8. These values are fundamental and often used in solving trigonometric problems. 9. Remember, angles can be in degrees or radians, and conversion is: $$\text{radians} = \frac{\pi}{180} \times \text{degrees}$$ 10. Practice these basics to build a strong foundation in trigonometry.