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#1 2005-09-17 04:44:52
- mikau
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sketching arcsin, arccos, arctan, arccsc, arcsec, arccot
Sketching sine and cosine curves are relatively easy. You just need the vertical translation, the magnitude, the period, and the horizontal translation.
Sketching tangent curves are slightly more difficult.
But when it comes to sketching the arc forms of trigonometric functions, I don't really know what to do. I could just study the patern that develops with each one, but that teaches me little. I could plot the points one by one in a few spots by just inserting values into the function, but I think this is cheating. I'm not really sure what else I'm supposed to do.
A logarithm is just a misspelled algorithm.
#2 2005-09-17 04:48:53
- mikau
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Re: sketching arcsin, arccos, arctan, arccsc, arcsec, arccot
To restate what I just said in a slighty more organized form:
I think these excersizes are meant to teach you understand how the functions work, I understand why the curve is the way it is given a particular point, but I find I can't sketch it accurately without inserting values into the equation. But if I just try to sketch it generally, then I pretty much need to ignore whats happening and just sketch the pattern, which teaches me little.
A logarithm is just a misspelled algorithm.
#3 2005-10-01 22:26:59
- John E. Franklin
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Re: sketching arcsin, arccos, arctan, arccsc, arcsec, arccot
How about just turning your paper 90 degrees when going from a trig function to the arc or inverse trig function?
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#4 2005-10-01 23:54:59
- mathsyperson
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Re: sketching arcsin, arccos, arctan, arccsc, arcsec, arccot
To find the inverse graph of a function, draw the function and then reflect it with the line of symmetry being y=x. To John, I tried your method and it seems that it returns the inverse of the negative function. eg. y=sin x would become y=-arcsin x.
Why did the vector cross the road?
It wanted to be normal.
#5 2005-10-02 02:34:28
- John E. Franklin
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Re: sketching arcsin, arccos, arctan, arccsc, arcsec, arccot
I guess if it was tracing paper you could flip the paper over through y=x and look through the back.
Or a lightbox with normal paper, or a window with light on the other side.
Thanks for the info mathsyperson, the 90 degrees was just a guess. I knew the 2 axis were flipping somehow.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.