Defining Four More Functions

Trigonometry · Axiom Academy

LESSON Four More Trigonometric Functions Building on sine and cosine, we define tangent, cotangent, secant, and cosecant—and learn where each function is undefined. 1. Tangent: The Ratio Function Tangent represents the ratio of the y-coordinate to the x-coordinate on the unit circle. Think of it as "rise over run"—the slope of the line from the origin to the point on the circle. 2. Cotangent: The Flipped Ratio Cotangent is simply the reciprocal ratio of tangent—it's "run over rise" instead of "rise over run." This makes it the ratio of the x-coordinate to the y-coordinate. 3. Secant and Cosecant: The Reciprocals These functions are the reciprocals of cosine and sine, respectively. They measure the "hypotenuse" distances in right triangle interpretations, but their most important feature is understanding where they're undefined. We now have six trigonometric functions, each with specific domain restrictions:

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