View source for Manuals/calci/tan

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<div style="font-size:30px">'''TRIAL PAGE'''</div><br/>

For example TAN(1..100) can give an array of the results, which is the TAN value for each of the elements in the array. The array could be of any shape.

<math>f(x,r1,r2)=\Gamma[(r1+r2)/2](r1/r2)^r1/2*(x)r1/2-1/ Γ(r1/2)Γ(r2/2)(1+r1x/r2)^(r1+r2)/2,    

==Description==

<math>F(x,\lambda)=\begin{cases}
1-e^{-\lambda x} &, x \ge 0 \\
0 &, x<0
\end{cases}</math>

<math>{\frac{n(n+1)}{(n-1)(n-2)(n-3)}*\frac{\sum{\frac{(xi-\bar{x})^4}{s}}\frac{-3(n-1)^2}{(n-2)(n-3)}</math>

<math>\frac{n(n+1)}{(n-1)(n-2)(n-3)} \frac{\sum (xi-\bar{x})^4}{s}- \frac{3(n-1)^2}{(n-2)(n-3)}</math>

<math>\frac{\sum (xi-\bar{x})^4}{s}</math>


<math>\frac{-3(n-1)^2}{(n-2)(n-3)}</math>

== Examples ==
#'''Example 1'''
{| class="wikitable"
|+Spreadsheet
|-
! !! A !! B !! C !! D!! E
|-
! 1
| 2 || 3 || 7 ||9 || 15
|-
! 2
| 8 || 12 || 13 || 20 || 25
|-
! 3
| 14  || 3  || 9  ||6 || 15
|-
! 4
| 12 ||23  || 1  ||42 ||17
|-
! 5
| 11 || 20 || 9  ||78 || 25
|}

'''From the above table values:'''
 {| class="wikitable" 
 |+ =MMULT(3,A1:A3)
 |- 
 | 15
 | 21
 | 24
 |}
 {| class="wikitable"
 |+=MMULT(6,A4:C4)
 |- 
 | 24
 | -30
 | 54
 |}

#'''Example 2'''
{| class="wikitable"
|+Matrix A
|-
| 7 || 5
|-
| 2 || 3 
|-
| 6 || 0
|-
| 9 || 8    
|}

{| class="wikitable"
|+Matrix B
|-
| 8 || -4 ||11
|-
| 2 || 7  || 5   
|}

*Here Matrix A is of order 4x2 and Matrix B is of order 2x3.
*So the Product Matrix is of order 4x3. i.e 
 '''1st Row''' 7*8+5*2 = 66  ;  7*(-4)+5*7 = 7  ;  7*11+5*5 = 102
 '''2nd Row''' 2*8+3*2 = 22  ;  2*(-4)+3*7 = 13  ;  2*11+3*5 = 37 and so on

*=MMULT(B2:C5,D2:F3) gives 

{| class="wikitable"
|+Result Matrix
|-
| 66 || 7 ||102
|-
| 22 || 13  || 37   
|-
| 48 || -24 || 66
|-
| 88 || 20  || 139 
|}

<math>\frac{\binom{m}{x}  \binom{N-M}{n-x}}{\binom{m}{x}}</math>

==trial==
<math>F(x,\mu,σ)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-μ)}{σ\sqrt{2}}\right)\right ]= φ\left[\frac{ln(x)-μ}{σ}\right ]</math>

<math>F(x,\mu,\sigma)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-\mu)}{\sigma \sqrt{2}}\right)\right ]= \varphi\left[\frac{ln(x)-\mu}{\sigma}\right ]</math>

\begin{bmatrix}
a & b \\
c & d \\
\end{bmatrix}

Then |A|=a|e   f     -b|d    f      +c|d    e
           h   i|       g    i|        g    h|

<math>a\begin{vmatrix}
e & f \\
h & i 
\end{vmatrix} -b\begin{vmatrix}
d & f \\
g & i 
\end{vmatrix} +c\begin{vmatrix}
d & e \\
g & h 
\end{vmatrix}</math>

==Trial 2==
<math>f(x,r1,r2)=Γ[(r1+r2)/2](r1/r2)^{r1/2}*(x)^{r1/2-1}/ Γ(r1/2)Γ(r2/2)(1+r1x/r2)^(r1+r2)/2</math>

<math>f(x,r1,r2)=\frac{\Gamma[\frac{r1+r2}{2}](\frac{r1}{r2})^{\frac{r1}{2}}}{ \Gamma(\frac{r1}{2})\Gamma(\frac{r2}{2})}*\frac{(x)^{\frac{r1}{2}-1}}{(\frac{1+r1x}{r2})^{\frac{r1+r2}{2}}}</math>

:<math>f(x,r_1,r_2)=\frac{\Gamma[\frac{r_1+r_2}{2}](\frac{r_1}{r_2})^{\tfrac{r_1}{2}}}{ \Gamma(\frac{r_1}{2})\Gamma(\frac{r_2}{2})}*\frac{(x)^{\tfrac{r_1}{2}-1}}{(\frac{1+r_1x}{r_2})^{\tfrac{r_1+r_2}{2}}}</math>
==trial==
1..10@DSIN

{| class="wikitable"
|-
! v11031 !! DSIN 
|-
| 1 || 0.01745240643728351 
|-
| 2 || 0.03489949670250097 
|-
| 3 || 0.05233595624294383 
|-
| 4 || 0.0697564737441253 
|-
| 5 || 0.08715574274765817 
|-
| 6 || 0.10452846326765346 
|-
| 7 || 0.12186934340514748 
|-
| 8 || 0.13917310096006544 
|-
| 9 || 0.15643446504023087 
|-
| 10 || 0.17364817766693033 
|}
==TRIAL3==
:<math>s_{x1}.s_{x2} = \sqrt{\frac{1}{2}(s_{x1}^2+s_{x2}^2)}</math>
<math>s_x_1</math>
<math>F(x,\alpha,\beta) = 1-e^-{(\frac{x}{\beta})}^\alpha</math>

<math>P(x)=
\begin{cases}
0 &for &x<a \\
1/b-a & for &a<x<b \\
0    &for &x>b    
\end{cases}</math>

<math>f(n) = 
\begin{cases} 
n/2,  & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}</math>

<math>
\begin{bmatrix}
a_{11} & A_{21}^{T}\\
A_{21} & A_{22}
\end{bmatrix}
=
\begin{bmatrix}
l_{11} & 0\\
L_{21} & L_{22}
\end{bmatrix}

\begin{bmatrix}
l_{11} & L_{21}^{T}\\
0  & L_{22}^{T}
\end{bmatrix}
=
\begin{bmatrix}
l_{11}^{2} & L_{11}L_{21}^{T}\\
 L_{11}L_{21} & L_{21}L_{21}^{T} + L_{22}L_{22}^{T}
\end{bmatrix}
</math>

==Description==
*This function gives the probability of the uniform distribution. 
*Uniform distribution is a symmetric probability distribution. 
*It is also called rectangular distribution. 
*In <math>UNIFORMDISTRIBUTED(x,ll,ul)</math> ,<math> x </math> is the numeric value to find the probability of the distribution, <math>ll </math> is the lower limit value and <math> ul </math> is the upper limit value. 
*The probability density function of the uniform distribution in the interval [a,b] are :
<math>P(x)= 
\begin{cases}
0 &for &x<a \\
1/b-a & for &a<x<b \\
0    &for &x>b    
\end{cases}</math>

==Video==
{{#ev:youtube|dMH0bHeiRNg|100|left|this is a test videos}}
{{#ev:youtube|KkgvmzY50Ag|200|right|this is a test videos}}
{{#ev:youtube|dMH0bHeiRNg|300|left|this is a test videos}}
{{#ev:youtube|dMH0bHeiRNg}}

{{#ev:vimeo|88296877}}
{{media:khanacademy|link=https://www.khanacademy.org/embed_video?v=9VZsMY15xeU" allowfullscreen webkitallowfullscreen mozallowfullscreen}}

9VZsMY15xeU

==Video1==
{{#ev:vimeo|88296877}}

{{#evt:
service=khanacademy
|id=https://www.khanacademy.org/embed_video?v=9VZsMY15xeU
|alignment=right
}}



{{#ev:youtube|9VZsMY15xeU}}

==Trial 5==
:<math>\left [\frac{redemption}{\left (1+\frac{yld}{frequency}\right )^{\left (N-1+\frac{DSC}{E}\right )}}\right ] +
\left [\dfrac{100*\frac{rate}{frequency}*\frac{DFC}{E}}{\left (1+\dfrac{yld}{frequency}\right )^{\left (\dfrac{DSC}{E}\right )}}\right ]
+
\left [\sum_{k=2}^N\dfrac{100*\frac{rate}{frequency}}{\left (1+\dfrac{yld}{frequency}\right )^{\left (k-1+\dfrac{DSC}{E}\right )}}\right ]
-
\left [100*\frac{rate}{frequency}*\frac{A}{E}\right ] </math>

Another Equation
:<math>\left [\frac{redemption}{\left (1+\frac{yld}{frequency}\right )^{\left (N+N_3+\frac{DSC}{E}\right )}}\right ] +
\left [\dfrac{100*\frac{rate}{frequency}* \sum_{i=1}^{NC}\dfrac{DC_i}{NL_i}}{\left (1+\dfrac{yld}{frequency}\right )^{\left (N_3+\frac{DSC}{E}\right )}}\right ]
+
\left [\sum_{k=1}^N\dfrac{100*\frac{rate}{frequency}}{\left (1+\dfrac{yld}{frequency}\right )^{\left (k-N_2+\dfrac{DSC}{E}\right )}}\right ]
-
\left [100*\frac{rate}{frequency}* \sum_{i=1}^{NC}\frac{A_i}{NL_i}\right ] </math>

==Trial 6==
<math>\left [\dfrac{\left (redemption + \left (\left(\sum_{i=1}^{NC}\frac{DC_i}{NL_i}\right )*\frac{100*rate}{frequency}\right )\right )-\left (par + \left ( \left (\sum_{i=1}^{NC}\frac{A_i}{NL_i}\right )*\frac{100*rate}{frequency}\right )\right )} {par + \left ( \left (\sum_{i=1}^{NC}\frac{A_i}{NL_i}\right )*\frac{100*rate}{frequency}\right )}\right ]
*
\left [\frac{frequency}{\left(\sum_{i=1}^{NC}\frac{DSC_i}{NL_i}\right )}\right ]</math>


<math>f(x,\mu,\sigma)=\frac {1}{\sigma\sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}</math>

==Trial==
<math>\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx </math>

<math> \frac{1}{\Gamma(s)} \int\limits_{0}^{\infty}\frac{x^{s-1}}{e^{x-1}}\,dx </math>

{| border="1" cellpadding="5" cellspacing="0"
|-
| 1 || 2 || 3 || 4 
|-
| rowspan="2"| 
 5 6 7 
 5 6 7
|-
| 0 || 0 || 0 
|-
| rowspan="2"| 
 5 6 7 
 5 6 7
|-
| 0 || 0 || 0 
|}

==DOC==
{|border="1" cellpadding="5" cellspacing="0"
|-
! Functions !! Parameters
|-
| $ ||
|-
| $$ ||
|-
| $$$ ||
|-
| $$F ||
|-
| $A ||
|-
| $C ||
|-
| $CELLS ||
|-
| $R ||
|-
| $X ||
|-
| $_ ||
|-
| $d ||
|-
| $diag ||
|-
| $dth ||
|-
| $x ||
|-
| X$ ||
|-
| ZJSON ||
|-
| __$ ||
|-
| ac ||
|-
| accumulate ||
|-
| accumulatewith ||
|-
| across ||
|-
| add ||
|-
| addcolumn ||
|-
| addrow ||
|-
| addsequence ||
|-
| adjoint ||
|-
| aggregate ||
|-
| any ||
|-
| appendfunction ||
|-
| ar ||
|-
| async ||
|-
| atindex ||
|-
| atnode ||
|-
| backward ||
|-
| bindcolumn ||
|-
| branch ||
|-
| branchvalues ||
|-
| c ||
|-
| calci ||
|-
| car ||
|-
| cartesianproduct ||
|-
| cdr ||
|-
| cell ||
|-
| cells ||
|-
| checktype ||
|-
| chunks ||
|-
| ci ||
|-
| clean ||
|-
| clear ||
|-
| clearcopy ||
|-
| clearrepeats ||
|-
| clone ||
|-
| colconcat ||
|-
| colcount ||
|-
| collect ||
|-
| collectasvector ||
|-
| collectwhile ||
|-
| collectwhileasvector ||
|-
| column ||
|-
| columnconcat ||
|-
| columns ||
|-
| compare ||
|-
| concatall ||
|-
| converge ||
|-
| copy ||
|-
| core ||
|-
| count ||
|-
| crosstab ||
|-
| cube ||
|-
| cumcolumn ||
|-
| cumcolumns ||
|-
| cumcolumnswith ||
|-
| cumcolumnwith ||
|-
| cumrow ||
|-
| cumrows ||
|-
| cumrowswith ||
|-
| cumrowwith ||
|-
| cumulate ||
|-
| data ||
|-
| dc ||
|-
| deal ||
|-
| deepcopy ||
|-
| deletecolumn ||
|-
| deleterow ||
|-
| det ||
|-
| determinant ||
|-
| dim ||
|-
| div ||
|-
| divide ||
|-
| dr ||
|-
| drop ||
|-
| dropwhile ||
|-
| dropwhileasvector ||
|-
| eighteenth ||
|-
| eighth ||
|-
| eleventh ||
|-
| equal ||
|-
| equalvalues ||
|-
| eval ||
|-
| except ||
|-
| exec ||
|-
| explode ||
|-
| extract ||
|-
| few ||
|-
| fifteenth ||
|-
| fifth ||
|-
| fillwith ||
|-
| filtermatches ||
|-
| filteroncolumn ||
|-
| filteroncondition ||
|-
| filteronrow ||
|-
| findcellref ||
|-
| first ||
|-
| firstelement ||
|-
| firsthalf ||
|-
| fixat ||
|-
| fjoin ||
|-
| flatten ||
|-
| flip ||
|-
| flipparts ||
|-
| fold ||
|-
| foldl ||
|-
| foldr ||
|-
| forward ||
|-
| fourteenth ||
|-
| fourth ||
|-
| fourths ||
|-
| funcjoin ||
|-
| gettype ||
|-
| graph ||
|-
| graphin ||
|-
| half ||
|-
| halves ||
|-
| hderef ||
|-
| head ||
|-
| headings ||
|-
| hindex ||
|-
| hundredth ||
|-
| i ||
|-
| ic ||
|-
| ids ||
|-
| implode ||
|-
| inc ||
|-
| include ||
|-
| indices ||
|-
| injoin ||
|-
| insert ||
|-
| insertcolumn ||
|-
| insertrow ||
|-
| inverse ||
|-
| ir ||
|-
| is ||
|-
| is1d ||
|-
| is2d ||
|-
| isFalse ||
|-
| isTrue ||
|-
| islikelytype ||
|-
| isnotnull ||
|-
| isnull ||
|-
| istype ||
|-
| j ||
|-
| joincolumnswith ||
|-
| joinrowswith ||
|-
| joinwith ||
|-
| jq ||
|-
| keep ||
|-
| last ||
|-
| lastelement ||
|-
| list ||
|-
| lookup ||
|-
| make ||
|-
| make1to2d ||
|-
| makecore ||
|-
| makekeyarray ||
|-
| maplist ||
|-
| mapper ||
|-
| maprow ||
|-
| mask ||
|-
| match ||
|-
| matchcolumn ||
|-
| matchindex ||
|-
| matchrow ||
|-
| matchvalue ||
|-
| merge ||
|-
| mergecolumns ||
|-
| mergeio ||
|-
| mergerows ||
|-
| mid ||
|-
| millionth ||
|-
| multiply ||
|-
| nicejoin ||
|-
| nineteenth ||
|-
| nineth ||
|-
| nodeindex ||
|-
| notinclude ||
|-
| notwithinlimits ||
|-
| nth ||
|-
| ntimes ||
|-
| nullifyobjects ||
|-
| numbers ||
|-
| o ||
|-
| objects ||
|-
| of ||
|-
| otherthan ||
|-
| pack ||
|-
| pad ||
|-
| pair ||
|-
| pairmatch ||
|-
| partitiononcondition ||
|-
| parts ||
|-
| pastefolds ||
|-
| pick ||
|-
| pieces ||
|-
| pip ||
|-
| pipall ||
|-
| pipallwithslice ||
|-
| plot ||
|-
| prefix ||
|-
| primitives ||
|-
| print ||
|-
| printf ||
|-
| r ||
|-
| rand ||
|-
| random ||
|-
| remove ||
|-
| removeByVal ||
|-
| removeindices ||
|-
| removewith ||
|-
| repeatntimes ||
|-
| replace ||
|-
| replicate ||
|-
| rest ||
|-
| result ||
|-
| reverselevel ||
|-
| reversepip ||
|-
| reversesort ||
|-
| ri ||
|-
| rotate ||
|-
| rotatecolumns ||
|-
| rotaterows ||
|-
| row ||
|-
| rowconcat ||
|-
| rowcount ||
|-
| rowlengths ||
|-
| rowpush ||
|-
| rows ||
|-
| rslice ||
|-
| second ||
|-
| secondhalf ||
|-
| seq ||
|-
| set ||
|-
| setHeadings ||
|-
| setaxis ||
|-
| setcolumn ||
|-
| setrow ||
|-
| setunit ||
|-
| seventeenth ||
|-
| seventh ||
|-
| shiftlevel ||
|-
| shuffle ||
|-
| sixteenth ||
|-
| sixth ||
|-
| size ||
|-
| size2d ||
|-
| slices ||
|-
| slides ||
|-
| sortrecursively ||
|-
| sortwith ||
|-
| specialprint ||
|-
| spliteach ||
|-
| splitwhile ||
|-
| splitwhileasvector ||
|-
| stringlist ||
|-
| subtract ||
|-
| suchthat ||
|-
| suchthatasvector ||
|-
| suffix ||
|-
| t ||
|-
| table ||
|-
| tablelookup ||
|-
| tail ||
|-
| takewhile ||
|-
| takewhileasvector ||
|-
| tenth ||
|-
| third ||
|-
| thirds ||
|-
| thirteenth ||
|-
| thousandth ||
|-
| tofunctions ||
|-
| toobjectformat ||
|-
| totree ||
|-
| transpose ||
|-
| truefalse ||
|-
| twelfth ||
|-
| twentieth ||
|-
| twod ||
|-
| type ||
|-
| uncrosstab ||
|-
| unimplode ||
|-
| unimplodeleaf ||
|-
| unitsof ||
|-
| unwrapleaf ||
|-
| unzip ||
|-
| value ||
|-
| where ||
|-
| withinlimits ||
|-
| withouttail ||
|-
| x$ ||
|-
| xy ||
|-
| xypanel ||
|-
| z3 ||
|-
| zero ||
|-
| zip ||
|-
| zoompip ||
|}

==Trial New==
{| border="1" cellpadding="5" cellspacing="0"
|-
|
 5 6 7 
 5 6 7
| 0 || 0 || 0 
|-

|0 ||
 5 6 7 
 5 6 7
| 0 || 0 
|-

|1 || 0 ||

 5 6 7 
 5 6 7
|0 
|-

|| 0 || 0 || 0 ||

 5 6 7 
 5 6 7

|-
|}

==Trail 6==
<math>
\begin{bmatrix}
\alpha_1  & {\alpha_1}^q  & \cdots & {{\alpha_1}^q}^{n-1}  \\
\alpha_2  & {\alpha_2}^q  & \cdots & {{\alpha_2}^q}^{n-1}  \\ 
\alpha_3  & {\alpha_3}^q  & \cdots & {{\alpha_3}^q}^{n-1}  \\
\vdots & \vdots & \ddots & \vdots\\ 
\alpha_m  & {\alpha_m}^q  & \cdots & {{\alpha_m}^q}^{n-1} \\
\end{bmatrix}
</math>

*2. MATRIX("permutation",18).<math>\$</math>_(SUM) = 18
*3. MATRIX("permutation",5).<math>\$$$</math>(SUM)= 
*4. MATRIX("permutation",5).<math>\$$</math>(SUM) =
==Trail 7==
{| border="0"
|+''A table in a table''
|-
| [[File:Smoothed_Cursive_free_line_1.jpg|100px|thumb|center|Smoothed Cursive Free Line]]
| [[File:Smoothed_Cursive_free_line_1.jpg|100px|thumb|center|Smoothed Cursive Free Line]]
|-
|}
{| border="0" style="background:#ffdead;"
| align="center" colspan="2" |
[[File:Smoothed_Cursive_free_line_1.jpg|400px|thumb|center|Smoothed Cursive Free Line]]
|}
==Trial 8==

==Trial 3==