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# arcsin[sin(2pi/3)] Watch

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

PLS
Posted from TSR Mobile
2. 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
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
I understand where you're coming from but the solution is pi/3...

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

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

But this sort of question just requires you to know the way the trig curves work
5. (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
6. (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
That is only correct within the range of the arcsin function, which is -pi/2 <= arcsin(x) <= pi/2. In other words:

7. (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)

8. Aaah, now I see.

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...

Posted from TSR Mobile
9. (Original post by QuantumSuicide)
Can somebody provide a step by step solution for this with the CAST method

PLS
Posted from TSR Mobile
Code:
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
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:

^^^^^^^^^|^^^^^^^^^^|^^^^^^^^
_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].
10. (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
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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