Problem with Sines on both sides

[PerryKid]

Homework Statement

Solve for ∅

1.33 sin 25.0° = 1.50 sin ∅

Homework Equations

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.

 

[SteamKing]

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]

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

 

[PerryKid]

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)

 

[Simon Bridge]

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]

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]

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

 

[SammyS]

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]

"Law of sines" is usually derived on a scalene triangle - so the angle range is 0-pi.
The other clue is that this is "introductory physics homework"... where else would this structure come up?

If this question were posted in an algebra, or signals processing (say), context, I'd have had to bring up the periodicity next. No need to provide everything in one go - one step at a time huh? ;)

Nice heads up though.