Tangent Is a Slope, Not a Wave

You'll learnto understand tangent as the slope of the terminal ray.

Sine and cosine are coordinates. Tangent is their quotient, which makes it the slope of the terminal ray, and the slope picture explains everything that makes tangent behave unlike its two parents: a period of only π, walls where cosine dies, and no amplitude to speak of.

8 STEPS · 6 QUICK CHECKS · SLOPE · PERIOD π · ASYMPTOTES · NO AMPLITUDE · v2

tangent is a slope, not a wave

Before you start

What you're looking at

A single ray in Quadrant I with its rise and run measured into a slope.

The question

As the ray swings toward vertical, what happens to its slope?

Watch for

The slope growing without bound, and the undefined value at π/2 shown numerically before the asymptote is drawn.

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