Section+1.10

__**Secants**__
 * A secant is a line that crosses a circle in two place.


 * In the photo above, the length of the blue segment is the same value as the secant of the angle between the blue and purple segments. (The green segent is a tangent to this unit circle.) However, the legnth of the blue segment will always be posotive since legnths never become negative. On the contrary, the secant can become negative, so really it's the absolute values of the legnth of the blue line and the secant of the angle that will equal eachother.
 * There cannot be a secant when the angle between the blue and purple lines is pi/2 or any odd multiple of pi/2 because at these values x will be 0. This is impossible because secant is 1/cos, and you can never divide anything by 0
 * Now let's take a closer look at why this all works:
 * 1) We know that segent OR and OQ are both one because this illustration is on a unit circle.
 * 2) We also know that OP is the cosine of angle theta and QP is the sine of angle theta, also because this image is on a unit circle.
 * 3) We know that SR is the tangent of angle theta
 * 4) So since, OS/OR=OQ/OP (because of similar triangles) we can conclude that OS/1=1/cos(theta) and therefore OS=sec(theta)

Here is a graph of secant(x):


 * Notice how there is nothing between 1 and -1. This is because cosine is between 1 and -1 and when you divide that by something even smaller than one (to get secant) you end up with a number bigger than 1 or smaller than -1. Graphically, it is because the smallest OS can ever be is one.