Beyond Sine and Cosine

Trigonometry · Axiom Academy

Discover how four more trigonometric functions emerge naturally from the sine and cosine you already know! Let's begin with sine and cosine on the unit circle. Move the slider to explore how these familiar functions change with angle! The First New Function: Tangent What if we divide sine by cosine? This ratio creates a new function with its own geometric meaning! Four More Functions from Division By dividing sine and cosine in different ways—and taking their reciprocals—we get four new trigonometric functions. Click each card to highlight it! Change the angle and watch how all six functions relate to each other. Notice when functions become very large or undefined! The Complete Trigonometric Family

This is the written version of the interactive lesson above. See the full Trigonometry course.