How are circles and triangles related?

Often trigonometry is taught in relation to triangles. sine and cosine just kind of magically show up in discussion without really explaining their relevance.

After watching this video from 3blue1brown it clicked for me how circles and triangles are related (in this case in 2 dimensions).

Short answer:

• sin(θ) measures your vertical distance on a unit circle for the angle θ (the y value between -1 and 1)
• cos(θ) measures your horizontal distance on a unit circle for the angle θ (the x value between -1 and 1)

To help with this intuition, here's an interactive unit circle (radius = 1 centered on the origin (0, 0)) that shows the relationship between sine, cosine, circles and triangles all in one interactive infographic.