Relationships Between Sine, Cosine, and Tangent of the Same Angle
🎯 The Big Idea
Sine, cosine, and tangent are not independent — they are deeply connected through elegant mathematical relationships. Understanding these connections gives you powerful tools for simplifying expressions and solving equations.
Prerequisites:
- Definition of sin, cos, tan
- Right triangle trigonometry
- The unit circle concept
📐 Starting from the Right Triangle
Consider a right triangle with angle $\theta$, opposite side $a$, adjacent side $b$, and hypotenuse $c$:
Basic Definitions:
$$\sin\theta = \frac{a}{c} \quad \text{(opposite / hypotenuse)}$$
$$\cos\theta = \frac{b}{c} \quad \text{(adjacent / hypotenuse)}$$
$$\tan\theta = \frac{a}{b} \quad \text{(opposite / adjacent)}$$
Interactive visualization — available in the full lesson