[6.49] Taylor() Polynomial Function Finds Tangent Line - Texas Instruments TI-89 Tip List

Neither of these results are useful.
A more elaborate function can be written which also handles list and matrix arguments:
atan2(αx,αy)
Func
©(x,y) 4-quadrant arctan(y/x)
©Must be installed in math\
©6jan02/dburkett@infinet.com
local αt,εm,τx
"atan2 error"→εm
define αt(α,β)=func
when(α=0 and β=0,undef,R▶Pθ(α,β))
endfunc
getType(αx)→τx
if τx≠getType(αy):return εm
if τx="LIST" then
if dim(αx)≠dim(αy):return εm
return seq(αt(αx[k],αy[k]),k,1,dim(αx))
elseif τx="MAT" then
if rowdim(αx)≠rowdim(αy) or coldim(αx)≠coldim(αy):return εm
return list▶mat(math\atan2(mat▶list(αx),mat▶list(αy)),coldim(αx))
elseif τx="NUM" then
return αt(αx,αy)
else
return εm
endif
EndFunc
Both arguments of atan2() must be the same type, and must be numbers, lists or expressions. atan2()
does not work with symbolic arguments.
Typical calls and results in Degree angle mode are:
atan2(1,1)
atan2(-1,-1)
atan2({1,-1},{1,-1})
1 −1
a tan 2
0 3

[6.49] Taylor() polynomial function finds tangent line

The line tangent to a function y = f(x) at a point x = a is defined by the criteria that the line passes
through point (a,f(a)) and the slope of the line is the derivative of f(x) at x = a. If the tangent line is
y = m $ x + n
returns
returns
returns
1 1
,
0 3
© Function name, error message, αx type
© Initialize error message
© Function finds atan2() of simple elements
© Save argument type for later tests
© Return error if arguments not same type
© Handle list arguments
© Handle matrix arguments
© Handle numeric arguments
© Return error for all other arg types
45
-135
{45,-135}
45
returns
undef 30
© Validate dimensions
135
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