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    sorry if wrong section but I have a couple questions;


    when solving trig equations, in range -180 degrees to 180 degrees, or pi to 2pi, for example,
    what should be used in relation to inverse cos (I understand sin and tan) to find the solutions of theta (p being the principle value for inverse sin cos tan)

    basically for cos,

    one books saying this;

    degrees..........radians
    -360+p..........-2pi+p
    -p............-p
    p.........p
    360-p..........2pi-p
    360+p..........2p+p

    (sorry, don't know how to do a table but I'm sure you get the point)


    whereas another book is using 180 degrees, instead of 360, to calculate a solution? eg, using 180-p for some reason? instead of adding theta to -360 or taking it away from 360?

    ___________
    also another quick Q, when finding solutions in the range 0 to 2pi, or -pi to pi, etc etc..
    can you leave the answers/solutions in decimals or do you have to put it in terms of pi? the textbook is giving me answers in terms of pi when questions involving the ranges from pi to pi, e,g "(5pi)/6", and I have no idea how to get it in terms of pi so would just putting "2.62" (radians) be fine? as of course this is fine when question is asking in degrees (with answer in deg, of course).


    sorry if the questions I'm asking are unclear, but I'd be very grateful if a math wiz could help, thanks
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    (Original post by sakzn)
    sorry if wrong section but I have a couple questions;


    when solving trig equations, in range -180 degrees to 180 degrees, or pi to 2pi, for example,
    what should be used in relation to inverse cos (I understand sin and tan) to find the solutions of theta (p being the principle value for inverse sin cos tan)

    basically for cos,

    one books saying this;

    degrees..........radians
    -360+p..........-2pi+p
    -p............-p
    p.........p
    360-p..........2pi-p
    360+p..........2p+p

    (sorry, don't know how to do a table but I'm sure you get the point)


    whereas another book is using 180 degrees, instead of 360, to calculate a solution? eg, using 180-p for some reason? instead of adding theta to -360 or taking it away from 360?
    When you have \cos(x)=a then the solutions here are x=2\pi n \pm \arccos(a) (arccos meaning the inverse cos function) where n \in \mathbb{Z}, so choosing n=-1 or n=1 or n=-2 or so will give you the nearby solutions to the principal value which is when n=0. In basic terminology, you keep adding OR subtracting 2 \pi continuously from both \arccos(a) and -\arccos(-a) - which is what your table is doing.

    Works the same for degree as you'd expect, since \pi^{\text{c}} = 180^{\circ} so we can easily convert.

    ___________
    also another quick Q, when finding solutions in the range 0 to 2pi, or -pi to pi, etc etc..
    can you leave the answers/solutions in decimals or do you have to put it in terms of pi? the textbook is giving me answers in terms of pi when questions involving the ranges from pi to pi, e,g "(5pi)/6", and I have no idea how to get it in terms of pi so would just putting "2.62" (radians) be fine? as of course this is fine when question is asking in degrees (with answer in deg, of course).

    Better to leave it in terms of \pi, or otherwise exact answer.

    If you have a specific question which asks you to express the answer in terms of \pi that you couldn't do, you can post it here and I'll walk you through it.
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    (Original post by RDKGames)
    When you have \cos(x)=a then the solutions here are x=2\pi n \pm \arccos(a) (arccos meaning the inverse cos function) where n \in \mathbb{Z}, so choosing n=-1 or n=1 or n=-2 or so will give you the nearby solutions to the principal value which is when n=0. In basic terminology, you keep adding OR subtracting 2 \pi continuously from both \arccos(a) and -\arccos(-a) - which is what your table is doing.

    Works the same for degree as you'd expect, since \pi^{\text{c}} = 180^{\circ} so we can easily convert.




    Better to leave it in terms of \pi, or otherwise exact answer.

    If you have a specific question which asks you to express the answer in terms of \pi that you couldn't do, you can post it here and I'll walk you through it.

    thanks so much for the help, you're brilliant!

    however, how do I exactly convert into \pi ?

    sorry if it sounds a bit silly. Just that when I get an answer I haven't an idea!

    e.g,
    [insert Q here within range 0-2



and I get sin(theta)=1/2 and sin(theta)=-1

do the inverse, and theta is then 0.52 or -1.57

I then deduce the solutions to be 0.52, 2.62 and 4.71

.. however the book saying the answers [tex\pi/6, 5/6 and 3[tex\pi/2 .. which is equivalent to my answers but how do I get it into [tex\pi[/tex]? thanks!
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    the simplest thing is to sketch the cos graph, mark on the answer your calculator gives you & see where else you would get a similar result ( draw a horizontal line at the correct height )
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    gah I posted a long post but saying its being reviewed.

    thanks so much for the help, you're brilliant!

    +basically what i wanted to also ask is how do I convert it into pi?
    [insert Q here from range of 0-2pi]
    i get sin(theta)=1/2 and sin(theta)=-1
    inverse then gives 0.52 or -1.57..
    so I deduce the solutions to be 0.52, 2.62 and 4.71
    .. however the answers in book saying pi/6, 5pi/6 and 3pi/2, which is of course equivalent but I have no idea how to get it into that form?
    thanks!
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    (Original post by the bear)
    the simplest thing is to sketch the cos graph, mark on the answer your calculator gives you & see where else you would get a similar result ( draw a horizontal line at the correct height )
    that is helpful too, didnt think of doing that, thanks also!
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    (Original post by sakzn)
    gah I posted a long post but saying its being reviewed.

    thanks so much for the help, you're brilliant!

    +basically what i wanted to also ask is how do I convert it into pi?
    [insert Q here from range of 0-2pi]
    i get sin(theta)=1/2 and sin(theta)=-1
    inverse then gives 0.52 or -1.57..
    so I deduce the solutions to be 0.52, 2.62 and 4.71
    .. however the answers in book saying pi/6, 5pi/6 and 3pi/2, which is of course equivalent but I have no idea how to get it into that form?
    thanks!
    Well from \sin(x)=\frac{1}{2} you should get x=\frac{\pi}{6} as the exact answer, no need to put it in decimals.

    Then another solution, since its sine, is given by \pi - \frac{\pi}{6}=\frac{5}{6}\pi


    Repeat similarly for the -1 solution




    Further solutions are given by adding/subtracting 2\pi continuously from the two above.


    Generally, just like cosine, sine has general solutions whereby if \sin(x)=a then:

    x=2\pi n + \arcsin(a)
    x=2 \pi n + \pi - \arcsin(a)
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    (Original post by RDKGames)
    Well from \sin(x)=\frac{1}{2} you should get x=\frac{\pi}{6} as the exact answer, no need to put it in decimals.

    Then another solution, since its sine, is given by \pi - \frac{\pi}{6}=\frac{5}{6}\pi


    Repeat similarly for the -1 solution




    Further solutions are given by adding/subtracting 2\pi continuously from the two above.


    Generally, just like cosine, sine has general solutions whereby if \sin(x)=a then:

    x=2\pi n + \arcsin(a)
    x=2 \pi n + \pi - \arcsin(a)
    ah that makes more sense, thank you
 
 
 
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