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

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- February 7th 2011, 01:51 AMprasumcomplex 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 - February 7th 2011, 02:13 AMemakarov
Is there somewhere in this formula?

- February 7th 2011, 04:46 AMHallsofIvy
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? - February 7th 2011, 05:58 AMSoroban
Hello, prasum!

Quote:

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.