(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the value of ArcSin[2].

NOTE: This question was asked in: https://www.physicsforums.com/showthread.php?t=226670 I made a new thread since I wasn't sure about my solution and didn't want to confuse the OP or anybody else.

2. Relevant equations

[tex]

e^{i \theta} = \cos{(\theta)} + i \sin{(\theta)}

[/tex]

3. The attempt at a solution

Let,

[tex]

ArcSin[2] = k

[/tex]

Then,

[tex]

Sin[k] = 2

[/tex]

Let,

[tex]

\lambda = \cos{(k)} + i \sin{(k)}

[/tex]

[tex]

\sin{(k)} = \frac{\lambda - \sqrt{1 - \sin(k)^2}}{i}

[/tex]

[tex]

\sin{(k)} = \frac{\lambda - \sqrt{1 - (2)^2}}{i}

[/tex]

[tex]

\sin{(k)} = \frac{\lambda - \sqrt{3}i}{i}

[/tex]

[tex]

2 = \frac{e^{ik}}{i} - \sqrt{3}

[/tex]

[tex]

e^{ik} = i(2 + \sqrt{3})

[/tex]

[tex]

k = \frac{1}{i} log_e(i(2 + \sqrt{3}))

[/tex]

[tex]

k = -i log_e(i(2 + \sqrt{3}))

[/tex]

My question is.. is this the right way to do it? Or.. all the assumptions that i've taken.. are they correct?

thanks.

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# Homework Help: ArcSin[2] {previously asked by a member}

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