# Thread: Solve the trigonometric equation?

1. ## Solve the trigonometric equation?

a) Solve the following trigonometric equation: A = cosX + AsinX, for some angle X.

b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX.

You will have used degrees to answer parts a and b. However, the mathematics below requires the use of radians. Convert degrees to radians by multiplying the degree measurement by π/180.

You will now find a value of i^i.

This will require the euler identity e^iX = cosX + isinX, part b) and exponent arithmetic.

c) Evaluate, for one value, i^i.

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So I honestly have no idea how to start this off haha. Could someone help out? Obviously you don't need to solve the whole thing - i just need to know how to start it off. Thanks!

2. ## Re: Solve the trigonometric equation?

Originally Posted by eleventhhour
a) A = cosX + AsinX, for some angle X.
b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX.
c) Evaluate, for one value, i^i.
I honestly have no idea what parts (a & b) are about. I only taught the for thirty years.

But I do know that $e^{(i\theta)}=\exp(i\theta)=\cos(\theta)+i\sin( \theta)$.

And $i^i=\exp(i\log(i))=\exp(\frac{-\pi}{2})$

3. ## Re: Solve the trigonometric equation?

A = cosX + AsinX, for some angle X.

Cos x = A ( 1- sin x )
Cos2x/2 – sin2 x/2 = A ( cos x/2 – sin x/2 )2
[Cos x/2 + sin x/2 ]/ [cos x/2 – sin x/2] = A
[ 1 + tan x/2 ]/[ 1- tan x/2 ] = A

1/[ tan ( π/4+ x/2 ) ] = A

I am sure now you can finish it

4. ## Re: Solve the trigonometric equation?

Hey, if you're looking for good resources, then I recommend to visit: https://www.youtube.com/watch?v=2P2_...KpJncYFke-V0xQ
Karol