I am having an issue with understanding the concept of a secant and to some extent a tangent. Yes all the basic trig functions are ratios, but the sine ratio represents an angle. I have seen diagrams representing a secant as a line, but it is something more abstract. I have divided the hypotenuse by the adjacent line, but 4.47 / 4 = 1.1... so obviously the value of 1.1 is much smaller than 4.47. Apparently, the secant line is longer than the hypotenuse in all the diagrams that I have seen ...so I am at a lost as to how a secant translates into the longer line.
Thanks for the reply grandad. It took a while, but I figured what my problem was. I was reading secant theta as the angle of secant instead of the secant OF theta. I was working on conversion between degrees and the trig ratios, so I was reading the ratios literally. It's not easy telling which context is used, but now that I am aware of the two different meanings, I should be able to tell. So anyhow, I figured out how to calculate the secant in a unit circle:
I let the hypotenuse equal the radius and divide it by the adjacent. Then once I get the angle, I let the adjacent equal the radius. Then I do the usual inverse operation to get the length of the hypotenuse that cuts through the circle, which of course is plainly the secant.