Trigonometric equation over unit circleLet us consider the equations p 0 2 + q 0 2 = 1 and − a p 0 sin ⁡ s + b q 0 cos ⁡ s = 0How do i solve for p 0 , q 0 ?

Question

Trigonometric equation over unit circleLet us consider the equations                    p        0              2    +                    q        0              2    =  1    and        −    a        p    0    sin  ⁡  s  +  b      q    0    cos  ⁡  s  =  0How do i solve for       p    0    ,      q    0  ?

Calvin Maddox · Accepted Answer

Let   s  =  0 so that we have   b      q    0    =  0, and by letting   s  =  π      /    2 we get   −  a      p    0    =  0. Then either   b  =  0 or       q    0    =  0. If the latter, then       p    0    ∈  {  −  1  ,  1  } by the first equation. Similarly, if       p    0    =  0 then       q    0    ∈  {  −  1  ,  1  }. So the solutions   (      p    0    ,      q    0    ) must be among   (  −  1  ,  0  ),   (  1  ,  0  ) if   a  =  0 and   (  0  ,  −  1  ),   (  0  ,  1  ) if   b  =  0. It is routine to verify that these are indeed solutions in the given cases.

gfresh86iop · Accepted Answer

Let us rewrite the system in the simple form      {                                        p            2                    +                      q            2                    =          1          ,                                      u          p          =          v          q          .                        Then      v    2        p    2    +      v    2        q    2    =      v    2  is  (      u    2    +      v    2    )      p    2    =      v    2    .The rest is yours.

Trigonometric equation over unit circle Let us consider the equations p_0^2+ q_0^2 =1 and-a p_0 sin s + b q_0 cos s = 0 How do i solve for p_0,q_0?

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