“We’re teaching math wrong” (part N/???)

When you were introduced to sine, cosine, and tangent, I’m going to bet you were introduced to them in terms of triangles. Maybe you remember learning “SOH-CAH-TOA” to keep it all straight. Then maybe much later in your curriculum they showed you the unit circle, radian measure, and had you memorize a bunch of facts about signs and quadrants, etc.

I’m here to tell you that your confusion was natural because they taught you the subject exactly backwards. Trigonometry proceeds from the circle first! There’s a reason it’s called the “tangent” kids—it’s the slope of the tangent line that touches the unit circle at whatever point bounds the arc you’ve chosen.

Once you get the Pythagorean theorem under your belt, we can explain the basic trig functions to you on the unit circle in a way that makes sense both visually and algebraically (whatever learning style you prefer).

Yet another example where math curricula are apparently designed by people who don’t understand math—historically or otherwise.