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I have a simple trig equation of

$cos(θ/2)=0.382$ and I'm trying to solve for theta, The correct value should be 0.37 radians for theta, but I can't seem to figure out how to get this, I tried doing the inverse cos of 0.382 but that gave me 1.18 radians instead, even if I divided that by 2 it's still not anything near 0.37.

What am I doing wrong?

EDIT: to clarify this question is from my quantum computing class on Qubits, this is one of the solutions to exercises I'm supposed to do: enter image description here

we are supposed to solve get the directions of the vectors on a bloch sphere given the qubit state, which is basically just solving for theta and phi, I don't think this should affect the trig part though, could the answer possibly be wrong?

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    [$\cos(0.37 / 2) \simeq 0.983$](http://www.wolframalpha.com/input/?i=cos(0.37+%2F+2)). – 2017-01-24
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    Are you allowed to use a calculater for the inverse cos? – 2017-01-24
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    $\cos^{-1}(.382) = 1.18$ so $\theta/2 = 1.18 $ so $\theta = 2.36$ (multiply not divide and check. $\cos (2.36/2) \eqapprox .380$ so.... I don't know. Why is the correct value supposed to by .37? – 2017-01-24
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    Please can you add some context, e.g. more of the original question? Clearly $\theta = 0.37$ is not a solution of $\cos(\frac{1}{2}\theta)=0.382$. Where did you get the $\cos(\frac{1}{2}\theta)$ and the $0.382$ from? Why do you think the answer is $0.37$? – 2017-01-24
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    I have edited my post with some clarification however I don't really think it affects anything – 2017-01-24

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Given that $\cos(0.37/2) \approx 0.983$ and that $0.983 \neq 0.382$, clearly the correct answer isn't going to be $\theta = 0.37$.

Your professor probably just made a mistake when writing the exercise. A correct solution to $\cos(\theta/2) = 0.382$ is $\theta \approx 2.3577$.