How to solve $cos(theta + angle)$ equation?

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I can't seem to figure out how to solve an equation similar to the one below.



$$cos(theta+fracpi3)=frac1sqrt3$$



The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.



$$theta+fracpi3=arccos(frac1sqrt3)$$



Am I missing a step when solving this equation?







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    up vote
    1
    down vote

    favorite












    I can't seem to figure out how to solve an equation similar to the one below.



    $$cos(theta+fracpi3)=frac1sqrt3$$



    The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.



    $$theta+fracpi3=arccos(frac1sqrt3)$$



    Am I missing a step when solving this equation?







    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I can't seem to figure out how to solve an equation similar to the one below.



      $$cos(theta+fracpi3)=frac1sqrt3$$



      The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.



      $$theta+fracpi3=arccos(frac1sqrt3)$$



      Am I missing a step when solving this equation?







      share|cite|improve this question












      I can't seem to figure out how to solve an equation similar to the one below.



      $$cos(theta+fracpi3)=frac1sqrt3$$



      The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.



      $$theta+fracpi3=arccos(frac1sqrt3)$$



      Am I missing a step when solving this equation?









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 11 at 0:36









      Matt Hough

      323




      323




















          2 Answers
          2






          active

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          up vote
          1
          down vote



          accepted










          Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
          Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)






          share|cite|improve this answer




















          • Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
            – Matt Hough
            Aug 11 at 2:06






          • 1




            Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
            – Sean Roberson
            Aug 11 at 3:04










          • @SeanRoberson Ahh yep I see. Thanks for that.
            – Matt Hough
            Aug 11 at 4:45

















          up vote
          0
          down vote













          $$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$



          Try going off of this.






          share|cite|improve this answer




















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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote



            accepted










            Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
            Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)






            share|cite|improve this answer




















            • Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
              – Matt Hough
              Aug 11 at 2:06






            • 1




              Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
              – Sean Roberson
              Aug 11 at 3:04










            • @SeanRoberson Ahh yep I see. Thanks for that.
              – Matt Hough
              Aug 11 at 4:45














            up vote
            1
            down vote



            accepted










            Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
            Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)






            share|cite|improve this answer




















            • Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
              – Matt Hough
              Aug 11 at 2:06






            • 1




              Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
              – Sean Roberson
              Aug 11 at 3:04










            • @SeanRoberson Ahh yep I see. Thanks for that.
              – Matt Hough
              Aug 11 at 4:45












            up vote
            1
            down vote



            accepted







            up vote
            1
            down vote



            accepted






            Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
            Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)






            share|cite|improve this answer












            Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
            Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Aug 11 at 0:44









            imranfat

            7,94441432




            7,94441432











            • Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
              – Matt Hough
              Aug 11 at 2:06






            • 1




              Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
              – Sean Roberson
              Aug 11 at 3:04










            • @SeanRoberson Ahh yep I see. Thanks for that.
              – Matt Hough
              Aug 11 at 4:45
















            • Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
              – Matt Hough
              Aug 11 at 2:06






            • 1




              Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
              – Sean Roberson
              Aug 11 at 3:04










            • @SeanRoberson Ahh yep I see. Thanks for that.
              – Matt Hough
              Aug 11 at 4:45















            Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
            – Matt Hough
            Aug 11 at 2:06




            Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
            – Matt Hough
            Aug 11 at 2:06




            1




            1




            Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
            – Sean Roberson
            Aug 11 at 3:04




            Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
            – Sean Roberson
            Aug 11 at 3:04












            @SeanRoberson Ahh yep I see. Thanks for that.
            – Matt Hough
            Aug 11 at 4:45




            @SeanRoberson Ahh yep I see. Thanks for that.
            – Matt Hough
            Aug 11 at 4:45










            up vote
            0
            down vote













            $$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$



            Try going off of this.






            share|cite|improve this answer
























              up vote
              0
              down vote













              $$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$



              Try going off of this.






              share|cite|improve this answer






















                up vote
                0
                down vote










                up vote
                0
                down vote









                $$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$



                Try going off of this.






                share|cite|improve this answer












                $$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$



                Try going off of this.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 11 at 0:45









                Rushabh Mehta

                1,287216




                1,287216






















                     

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