Trigonometric Pythagorean Relationships

Very short post today to illustrate something I’ve never considered before.  Everyone usually has a diagram to illustrate the Pythagorean relationship on the unit circle like below.  I’ve always also liked to show the secant, tangent etc. on the unit circle and talk about how the names reflect the actual geometry.  For instance the tangent really is a tangent line.   However,  it turns out that all three variants of the Pythagorean relationship are also expressed as triangles in the same diagram and this provides a nice way to organize things conceptually. Standard View Variant 1 Variant 2