> But sin, cos, tan, cotan, log and all their friends by themselves don't compute, they are just a different kind of notation for numbers. No, they are a notat

> But sin, cos, tan, cotan, log and all their friends by themselves don't compute, they are just a different kind of notation for numbers. No, they are a notation for ideas. The fact that they have numerical values associated with them is true but misses the point that trigonometric functions are primarily defined with respect to each other and with respect to certain geometric concepts. In other words, cos(0) equals 1, but 1 has many more meanings than just cos(0). I would much rather have a student tell me that tan(x) = sin(x) / cos(x) than to say tan(x) is just a number.