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How to convert the Euler formula in trigonometric form

Posted 11 years ago
I want to convert the following euler formula in trigonometric form
there is a command called ComplexExpand
But it will produce the undesired results

(1)
the instructions below the picture will differentiate the equation and then expand it
it will produce the undesired result 


f2 = D[f1[t],t] // ComplexExpand

(2)
 Desired  result 
r3'[t]*( Cos[q3[t]] + I Sin[q3[t]] )-
r1(q1)'[t]*( Cos[q1[t]] + I Sin[q1[t]] )+
r2(q2)'[t]*( Cos[q2[t]] + I Sin[q2[t]] )+
r3[t](q3)'[t]*( Cos[q3[t]] + I Sin[q3[t]] )
POSTED BY: Robert Chen
4 Replies
Posted 11 years ago
If i change the format of the equation

It will output the result  I want
I don't know why it would produce the different results

f[t_] = r2 E^(I q2[t]) + r3[t] E^(I q3[t]) - r1 E^(I q1[t])
f2 =  f'[t] // ComplexExpand
POSTED BY: Robert Chen
Hi, 

Also, try ExpToTrig[] 
f1 = D[r2 Expand[I q2[t]] + r3 Exp[I q3[t]] - r1 Exp[I q1[t]], t];
f1 // ExpToTrig
f1  // ExpToTrig  // TrigReduce (* also useful *)

I.M.
POSTED BY: Ivan Morozov
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POSTED BY: Moderation Team
Try using ComplexExpand on the expression.
POSTED BY: David Reiss
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