Question: Can we ever have a trigonometric ratio that is larger than 1? Why or why not?

The sine and cosine are never more than 1. The secant, cosecant, tangent, and cotangent can be anything, from negative infinity to positive infiinity. You can read and learn about their definitions in terms of the unit circle, and everything will fall into place.

For sine and cosine, we can not have a trigonometric ratio that is larger than one. In tangent, the opposite can be longer than the adjacent w/out affecting the whole triangle.

(I almost forgot about cot, sec, and csc ... hehe)

If sine and cosine are always less than one, then sec and csc are going to always be greater than one.

For tan and cot, it really depends on the sides ...