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Really quick question about Trig!

If I've got $\sin^{-1}(1)$ or $\sin^{-1}(2)$, how would I convert that to $90^\circ$ and $180^\circ$ ?

I'm trying to convert a graphed version of $f(x) = \sin(x)$ in the domain $0 \leq x \leq 360$ with all intersections of $\sin(x) = 0.371$ from the first intersection being $(0.38,0.371)$ to be $(\text{degree}, 0.371)$

Thank you! Any help is greatly appreciated! :)

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First note that $\sin^{-1}(2)$ is not possible because $-1 \leq \sin{x} \leq 1$. Next take $y = \sin^{-1}(1) \Rightarrow \sin(y) =1 \Rightarrow y = \frac{\pi}{2}$ as one of the value –  user9413 Nov 24 '11 at 10:15
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$\arcsin(2)=\frac{\pi}{2}-i\ln(2+\sqrt 3)$ is a complex number, and thus cannot be the same as $180^\circ$. $\arcsin(1)$ will yield either $90^\circ$ or $\pi/2$, depending on the setting of your computing environment. In any event, it is a simple matter to convert radians to degrees. We have the relation $\pi\text{ radians}=180^\circ$. –  J. M. Nov 24 '11 at 10:16
    
basically I'm asking how I convert the 1 to 90 and the 2 to 180 in a picture like this :) bbc.co.uk/scotland/learning/bitesize/standard/maths_ii/images/… thank you! –  David Nov 24 '11 at 10:18
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I see neither a 1 nor a 2 on the axes in the picture you've linked to. –  J. M. Nov 24 '11 at 10:19
    
I'm sorry* I meant vice versa* in the event that x=90, how would that be converted to x=1? sorry for the confusion! –  David Nov 24 '11 at 10:20

1 Answer 1

Let me venture a guess.... Since you've stated that $(0.38, 0.371)$ is a point on your graph of $y = \sin x$, your calculating device must be in radians mode. Indeed, $\sin(0.38) = 0.371$. Now the graph you've included as a link in the comments section shows $y = \sin x$ if the angle $x$ is measured in degrees. So when you say you want to convert $(0.38, 0.371)$ to $(degree, 0.371)$, then all you need is the conversion factor, $$ \mathrm{Degrees} = \mathrm{Radians} \times \frac{180^{\circ}}{\pi} $$

In particular, $0.38 \times \frac{180^{\circ}}{\pi} \approx 21.77^{\circ}$.

(Note, what is confusing about your post is your mention of $\sin^{-1} 1$ and $\sin^{-1} 2$, which have nothing to do with the rest of the stated question. Moreover, your graph shows the intersections of $y = \sin x$ with the line $y = 0.75$, so did you really mean to ask about the $x$-value(s) when $y = 0.75$?)

Hope this helps!

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