inverse trig (1 Viewer)

[{*(00)*}]

you may want to write this down on paper...lol

how do you prove that " the derivative of inverse sine (x/a) is = to

1/√a^2 - x^2

and -prove that the inverse of tan x =

the derivative of inverse tan x, times x - (x / 1+x^2)

this question may be related to simpson's rule because this is a part (b) question, in part (a) it asked us the integral of inverse tanx, between 2 and 0, using simpson's rule, 5 functional values, and finish with a 2 dp approx.

i found the answer to be:12.66 for (a) but still confused on (b) thankyou!

 

[Trev]

Let y=sin^-1(x/a)
siny=x/a
x=asiny
dx/dy=acosy
dy/dx=1/(acosy)
Use cosy=√(1-sin²y)=√(1-(x/a)²) to get the required result.

Similarly for y=tan^-1x
tany=x
dx/dy=sec²y
dy/dx=1/(sec²y)
sec²y=1+tan²y=1+x² etc.

Neither proofs use simpsons rule.

 

[{*(00)*}]

thanks for help, btw, do you know how to type in math functions on ms word?

 

[Mountain.Dew]

thanks for help, btw, do you know how to type in math functions on ms word?

in word, click on Insert > Object.

then, in the list, scroll down to Microsoft Equation 3.0, highlight it, then click ok.

 

[{*(00)*}]

whoa, thanks man you just increased my productivity about 10000000000000%,
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(and yes i am exaggeraring)...

 

[Slidey]

(and yes i am exaggeraring)...

You don't say.

Anyway, there's also certain character combinations recognised in text bodies like when you go to post.

A lollipop to the person who posts a list.

 

[SoulSearcher]

I'd post one, but is this for the major text bodies, or just these forums, because I certainly don't know the entire list for the major text bodies.

 

[alcalder]

¹ = alt 0185
º = alt 0186
± = alt 0177
² = alt 0178
³ = alt 0179
¼ = alt 0188
½ = alt 0189
¾ = alt 0190
÷ = alt 0247

Is that what you meant? Things like greek letters and integral signs do not have "alt" codes.

 

[Slidey]

OK, here's the list I was thinking of. I recall KFunk using these combinations. However, they don't display correctly in my browser, so I'm lead to assume he used different ones.

http://barzilai.org/math_sym.htm

Oh well here's a nice list for those who don't mind copying and pasting:

http://www.unics.uni-hannover.de/nhtcapri/mathematics.html