math
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math [2020/09/26 14:10] – admin | math [2023/08/12 04:40] (current) – [pages in this wiki] raju | ||
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- | ==== sec(x) + tan(x) | + | ==== correlation |
+ | t-statistic for correlation, | ||
+ | \[ | ||
+ | t = r \sqrt{\frac{n-2}{1-r^2}} | ||
+ | \] | ||
+ | The reverse equation is | ||
\[ | \[ | ||
- | \sec x + \tan x = \tan \left( | + | r = \frac{t}{\sqrt{t^2 + n-2}} |
\] | \] | ||
- | I came across this simplification while reading https:// | + | Derivation of the reverse equation: |
+ | \begin{align*} | ||
+ | & t = r \sqrt{\frac{n-2}{1-r^2}} & \\ | ||
+ | & \frac{t^2}{r^2} = \frac{n-2}{1-r^2} & \\ | ||
+ | & \frac{t^2}{n-2} = \frac{r^2}{1-r^2} & \\ | ||
+ | & \frac{t^2}{t^2 + n-2} = r^2 & \\ | ||
+ | & r = \sqrt{\frac{t^2}{t^2 + n-2}} & | ||
+ | \end{align*} | ||
+ | |||
+ | See also: | ||
+ | * https:// | ||
+ | ==== sec(x) + tan(x) ==== | ||
+ | |||
+ | \begin{align*} | ||
+ | \sec x + \tan x & = \tan \left( \frac{x}{2} + \frac{\pi}{4} \right) \\ | ||
+ | & = \sqrt{\frac{1 + \sin x}{1 - \sin x}} | ||
+ | \end{align*} | ||
+ | |||
+ | I came across this simplification while reading https:// | ||
+ | |||
+ | ==== pages in this wiki ==== | ||
+ | * [[fibonacci sequence]] | ||
+ | * [[Leibniz integral rule]] | ||
+ | |||
+ | ==== links I came across ==== | ||
+ | * What is the formula for sum of the p-th powers of the first n positive integers? | ||
+ | * Use Faulhaber' | ||
+ | * The formula involves binomial coefficients and Bernoulli numbers. | ||
+ | * See also: https:// | ||
+ | |||
+ | ==== pages with math outside of this wiki ==== | ||
+ | use cases | to copy paste syntax | ||
+ | * https:// | ||
+ | * https:// | ||
+ | * https:// |
math.1601129435.txt.gz · Last modified: 2020/09/26 14:10 by admin