# Problem with Sines on both sides

## Homework Statement

Solve for ∅

1.33 sin 25.0° = 1.50 sin ∅

Law of Sines?

## The Attempt at a Solution

I did this:

([STRIKE]1.33[/STRIKE] sin 25.0°)/[STRIKE]1.33[/STRIKE] = (1.50 sin ∅)/1.33
sin 25.0° = (1.50 sin ∅)/1.33

but I'm solving for ∅, so I modified a little:

(1.33 sin 25.0°)/1.50 = ([STRIKE]1.50 [/STRIKE]sin ∅)/[STRIKE]1.50[/STRIKE]
sin ∅ = (1.33 sin 25.0°)/1.50

I have a basic understanding of trigonometry (SOH CAH TOA) but I'm not too sure how to do this. Can I use an inverse sine to figure? Does the law of sines apply?

There is no triangle.

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SteamKing
Staff Emeritus
Homework Helper
The law of sines is irrelevant to solving for the unknown angle phi. If you want to solve for phi, then, yes, you must use an inverse sine in your calculations.

Simon Bridge
Homework Helper
You have/i] to use an inverse sign.
1st solve for ##\sin\phi## and then take the inverse sine of both sides.

You have/i] to use an inverse sign.
1st solve for ##\sin\phi## and then take the inverse sine of both sides.

So will this solve for ∅?

[STRIKE]sin-1[/STRIKE]([STRIKE]sin[/STRIKE] ∅) = sin-1((1.33 sin 25.0°)/1.50)
∅ = sin-1((1.33 sin 25.0°)/1.50)

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Simon Bridge
Homework Helper
Absolutely: ##\sin^{-1}(\sin\phi )=\phi## by definition, so if ##\sin\phi = x## then ##\phi=\sin^{-1}x## where ##x## stands for everything on the RHS.

Welcome to PF BTW :)

SammyS
Staff Emeritus
Homework Helper
Gold Member
Absolutely: ##\sin^{-1}(\sin\phi )=\phi## by definition, so if ##\sin\phi = x## then ##\phi=\sin^{-1}x## where ##x## stands for everything on the RHS.

Welcome to PF BTW :)
Actually, ##\sin^{-1}(\sin\phi )=\phi## is only true for

##\displaystyle \ \ -\,\frac{\pi}{2}\le\phi\le \frac{\pi}{2}\ .##

Simon Bridge
Homework Helper
Yah well - that would be the rest of the definition ... the geometry here is Snell's law.

SammyS
Staff Emeritus
Homework Helper
Gold Member
Yah well - that would be the rest of the definition ... the geometry here is Snell's law.
What you say makes perfect sense !

It would have helped if OP had mentioned what he/she was applying the "Law of Sines" to.

Simon Bridge