Thread: complex trigo

the value of 169e^(pi+sin(inverse)(12/13)+cos(inverse)(5/13))

i know de moivres theorem cosa+isina

but how to proceed with inverses

Is there somewhere in this formula?

Originally Posted by prasum

the value of 169e^(pi+sin(inverse)(12/13)+cos(inverse)(5/13))

i know de moivres theorem cosa+isina

but how to proceed with inverses

With no "i" Demoivre's theorem does not apply. I see nothing to do but evaluate that using a calculator.

If that was supposed to be
then use the fact that

Of course, . You should recognize that refers to an angle in a right triangle with "opposite side" 5 and "hypotenuse" 13. What is the length of the other leg? So what are the sine and cosine?

Hello, prasum!

Note that and are the same angle!

Code:

            *
           **
          * *
      13 *  * 12
        *   *
       *θ   *
      *******
         5 

Hence, the exponent is: .


But what is the point of all this?

We could have cranked out the answer on our calculator.