Solving \cos(z)=\frac52 and I'm trying to solve for z but I

Gwendolyn Willett

Gwendolyn Willett

Answered question

2022-01-16

Solving cos(z)=52
and I'm trying to solve for z but I keep going in circles. I know cosz=52=12eiz+eiz so then eiz+eiz=5 but then I'm stuck

Answer & Explanation

xandir307dc

xandir307dc

Beginner2022-01-19Added 35 answers

Note
cosz=cosh(iz+i2πn)=52
which leads to iz+i2πn=±cosh152 and the solutions
z=2πn±icosh152
RizerMix

RizerMix

Expert2022-01-20Added 656 answers

Taking t=eiz we get t+1t=5t25t+1=0t1,2=5±212
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

Solving the quadratic further z=±ilog(5+212) which is pure imaginary to which we add the real variable part 2πn making up the complex angle. Graphs of (cosx,52) do not intersect. It is interesting to note however that the real part corresponds to the closest points between the non-intersecting cosine curve and straight line.

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