The Walls Grow Out of the Zeros

You'll learnto build secant, cosecant, and cotangent by flipping a graph you already know.

Secant, cosecant and cotangent need no new circle: each is built by flipping one you already know. One discipline runs the whole topic. A reciprocal blows up where its parent hits zero, and it touches its parent at the peaks. Get those two places right and the graphs draw themselves.

8 STEPS · 6 QUICK CHECKS · RECIPROCALS · WALLS AT THE ZEROS · THE FORBIDDEN BAND · v2

the walls grow out of the zeros

Before you start

What you're looking at

A short table of parent values and their reciprocals: 1→1, 1/2→2, 0→undefined.

The question

What happens to the reciprocal where the parent hits zero, and where the parent is ±1?

Watch for

Reciprocal is not inverse — that confusion starts at the notation — and parent zeros turning into asymptotes.

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