# Thread: integral [and derivative] of tan x

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## integral [and derivative] of tan x

What would the integral of tan x look like on a graph?

2. Methinks it would look like the graph of -ln(|cos(x)|) as simple integration of tan(x) would show you., now just plot.

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Thanks for the info. Are there any real life applications for the integral of tan x.

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Plenty. Here's one. If you spin a pin at random around a fixed pivot at the origin until it stops (uniform distribution of angles), and then find the intersection of the line containing the pin and the line x=1, and record the y coordinate of the intersection (ignoring sign), and then study the distribution of these y-coords, it is discovered to be pathological - it has no density function. Observe that y = mod(tan A), where A is the angle of the pin with the X axis. A density function is required to be normalised to have an integral of 1, but the integral of tan x from 0 to 90 is infinite, so the density function doesn't exist. As a consequence, it has no mean. What this means is that for any value M you propose, if you spin the pin enough times (n) then the average of the values recorded will eventually exceed M.

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Are there any applications for the derivative of tan x relating to spheres.

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## derivative of tan x

Are there any practical applications to derivative of tan x, especially in regards to spheres?

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