What does the secant value represent?
I know that $$\sec = 1/\cos(\theta)$$ but really I do not know what this value represents, so I need your help. A clear example with images would be appreciated.
[Math] What does the secant value represent
calculusgeometry
Related Solutions
The dot product tells you what amount of one vector goes in the direction of another. For instance, if you pulled a box 10 meters at an inclined angle, there is a horizontal component and a vertical component to your force vector. So the dot product in this case would give you the amount of force going in the direction of the displacement, or in the direction that the box moved. This is important because work is defined to be force multiplied by displacement, but the force here is defined to be the force in the direction of the displacement.
$b$ represents the y-intercept of the line: where the line crosses the y-axis.
It can be found by setting $x = 0$ (the line crosses the y-axis when and only when $x = 0.$)
An example of such a line, $$y = 3x + \underbrace{7}_{\large b}$$ crosses the y-axis at the point $(0, 7)$.
When $x = 0$, you see that $y = 7 = b$.
Best Answer
In this image, notice that as $\theta$ grows from $0$ to a right angle, the segment labeled $\sec\theta$ grows from $1$ to $+\infty$, and if $\theta$ were to go from $0$ down to minus a right angle, $\sec\theta$ would also go from $1$ up to $+\infty$.
On the other hand $\tan\theta$ would go from $0$ (not $1$) to $+\infty$ in one case, and from $0$ down to $-\infty$ in the other case.
Notice that the tangent is the length of a segment that is tangent (touching but not crossing) to the circle and the secant is the length of a segment that is secant to (cutting across) the circle. The words come from the Latin words tangere and secare, meaning to touch and to cut.
(The second image treats the three "co-" functions. I drew these with xfig several years ago and uploaded them to Wikipedia, where they are seen in this article.)