Trigonometric Functions 9Ee63E

1. **Stating the problem:** Understand the basic concepts of trigonometric functions. 2. **Definition:** Trigonometric functions relate the angles of a right triangle to the ratios of its sides. 3. **Main functions:** - 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. **Important rules:** - The hypotenuse is always the longest side. - Angles are measured in degrees or radians. - The functions are periodic and have specific ranges. 5. **Example:** For a right triangle with angle $$\theta$$, opposite side length $$3$$, adjacent side length $$4$$, and hypotenuse $$5$$: - $$\sin(\theta) = \frac{3}{5} = 0.6$$ - $$\cos(\theta) = \frac{4}{5} = 0.8$$ - $$\tan(\theta) = \frac{3}{4} = 0.75$$ 6. **Summary:** Trigonometric functions help find unknown sides or angles in right triangles using these ratios.