Trigonometri Problems at atand and acosd

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Andy Rahmawan
Andy Rahmawan 2012-10-18
Hi.. can you help me pls.. I have a problem :
54.8=acosd(20/(100-z))-atand(40/(500-z))
how to evaluate z at matlab? thanks..

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Matt Fig
Matt Fig 2012-10-18
编辑：Matt Fig 2012-10-18
This is perfect for the FZERO function....
fzero(@(z) 54.8-acosd(20./(100-z))+atand(40./(500-z)),30)
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Walter Roberson
Walter Roberson 2012-10-18
Caution: the above will only find a single solution at most, but there are two solutions (I say "at most" because there are two singularities and you need to watch out for the possibility that your guess is on the far side of a singularity from a solution.)
Matt Fig
Matt Fig 2012-10-18
Yes, Walter is correct. To see good initial guesses (and also a bad initial guess) for the solutions, look where the black line crosses the blue line:
x = 0:.01:500;
f = @(z) 54.8-acosd(20./(100-z))+atand(40./(500-z));
plot(x,f(x))
line([0 500],[0 0],'color','k')

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Walter Roberson
Walter Roberson 2012-10-18
You can use the symbolic toolbox if you have it.
Otherwise, rewrite the expression by subtracting the left-hand side from both sides, and then using a zero finder.
Note: there is more than one solution.

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