Trigonometri Problems at atand and acosd

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..

Answer 1

[Matt Fig]

This is perfect for the FZERO function....

fzero(@(z) 54.8-acosd(20./(100-z))+atand(40./(500-z)),30)

[Andy Rahmawan]

 fzero(@(z)  54.8-acosd(20./(100-z))+atand(40./(500-z)),30)

can you tell me where i can get value of 30? thanks

[Matt Fig]

30 is not a solution to your equation. I used 30 as an initial guess for FZERO. Have a look at the help for this function:

doc fzero

[Walter Roberson]

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]

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')

Answer 2

[Walter Roberson]

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.