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arcsin[sin(2pi/3)]

Can somebody provide a step by step solution for this with the CAST method

PLS
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Reply 1
arc sin just undoes what sin did?

So basically they cancel each other out :P

But obviously there is a general solution for the answer if you choose to do it and then undo it :smile:
Original post by Dingo749
arc sin just undoes what sin did?

So basically they cancel each other out :P

But obviously there is a general solution for the answer if you choose to do it and then undo it :smile:


I understand where you're coming from but the solution is pi/3...

Posted from TSR Mobile
Reply 3
Yeah because sin(2pi/3) = sin(pi/3) so it's just given the angle in its acute form :smile:

Thats what I mean by a general solution, for the trig functions there are infinitely many angles that give the same solution, your calculator should always give you the smallest one available :smile:

But this sort of question just requires you to know the way the trig curves work :smile:
Reply 4
Original post by QuantumSuicide
I understand where you're coming from but the solution is pi/3...

Posted from TSR Mobile


I dont know whether this is the correct method but i'll post it anyway,

If arcsin(2pi/3)

so sin(2pi/3) is what you want which is = root 3/2

if u want to then map this on the CAST diagram then 2pi/3 = 120 degrees, sin is positive in the second quadrant therefore 180-120= 60 degrees or pi/3
Original post by Dingo749
arc sin just undoes what sin did?

So basically they cancel each other out :P

But obviously there is a general solution for the answer if you choose to do it and then undo it :smile:


That is only correct within the range of the arcsin function, which is -pi/2 <= arcsin(x) <= pi/2. In other words:

arcsin(sinx))=x,providedπ2xπ2\arcsin(\sin x))=x, provided -\frac{\pi}{2}\le x\le\frac{\pi}{2}
(edited 9 years ago)
Reply 6
Original post by QuantumSuicide
I understand where you're coming from but the solution is pi/3...

Posted from TSR Mobile


Sin(2pi/3) is the same as sin(pi/3) as pi-(2pi/3)=pi/3 and sinx= sin(pi-x)
arcsin[sin(2π3)]arcsin[sin(\frac{2\pi}{3})]

=2nπ+2π3 or (2n+1)π2π3= 2n\pi + \frac{2\pi}{3} \ or \ (2n+1)\pi - \frac{2\pi}{3}
Aaah, now I see. :smile:

How would i go about solving things like arcsin(1/2) + arcsin(-1/2)... I don't understand what it really means to be honest...

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Reply 9
arcsin(x)=arcsin(x)\arcsin( -x ) = - \arcsin(x)
Original post by QuantumSuicide
Can somebody provide a step by step solution for this with the CAST method

PLS
Posted from TSR Mobile



Twice pi over three radians makes a hundred and twenty degrees.

*** * ***** ***** *****
* * ** * * * * * *
* *** * * * * * * * *
*** * * * * * * * * *****
* * * * * * *
*** * * ***** * * * *
^^^^^^^^^ * ***** * *
**** ***** * * * *
* * * * *
*** * * * *
* * * * * *
**** * ***** *****


Start sweeping on X axis of quadrant S; sweep
anti-clockwise. A sweep angle of 120 deg.
(sweep arm is marked in x's, angle measurement
in *'s) is in quadrant A. This means your sine
measurement, whatever it is, is POSITIVE.


.
_______________ . _________________
| | . | |
| | . | |
| | . |
+-------------+ . |________________
| xx | . |
| xx**|***.** |
| xx| . |* |
xx . |_*_____________|
..........................................
________________ . _____________
| . | \
| . | |
| . |
| . |
| . |
| . | |
| . | /
. ^^^^^^^^^^^^^


The sine value of 120 degrees is approximately
.866


Arc functions are REVERSE functions. CAVEAT: they
IGNORE angles greater than 90. You will get two
possible values out of an arc function if you know
the polarity of x.


.
_______________ . _________________
| | . | |
| | . | |
| | . |
+-------------+ . |________________
| | . |
| | . |
| | . | |
. |_______________|
..........................................
________________ . _____________
| . | \
| . | |
| . |
| . |
| . |
| . | |
| . | /
. ^^^^^^^^^^^^^


Here's a table:

Function | Quadrant | Result
^^^^^^^^^|^^^^^^^^^^|^^^^^^^^
_arc_cos_|____S_____|___neg.__|
_arc_cos_|____A_____|___pos.__|
_arc_cos_|____T_____|___neg.__|
_arc_cos_|____C_____|___pos.__|
_arc_sin_|____S_____|___pos.__|
_arc_sin_|____A_____|___pos.__|
_arc_sin_|____T_____|___neg.__|
_arc_sin_|____C_____|___neg.__|
_arc_tan_|____S_____|___neg.__|
_arc_tan_|____A_____|___pos.__|
_arc_tan_|____T_____|___pos.__|
_arc_tan_|____C_____|___neg.__|


o The arc sine of (the sine of [twice pi over three radians] or
[one hundred and twenty degrees]) is either [thirty degrees or
o o pi sixths] or [one hundred and twenty degrees or twice pi thirds].




Original post by Dingo749
arc sin just undoes what sin did?

So basically they cancel each other out :P

But obviously there is a general solution for the answer if you choose to do it and then undo it :smile:


Not totally. Sine-ing an angle and then arc sine-ing it loses some information. Let's say you sine 120 degrees and then you arc-sine the result. You'll actually end up with an answer of "30 degrees or 120 degrees" (but NOT 210 degrees or 300 degrees).

Same with cosine and tangent.

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