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While reading the general solutions of trigonometric equations, I came to this:

The equation $\sin\theta = k$ is satisfied by two values of $\theta$ of the form $\alpha$ & $\pi - \alpha$ in the interval $0 \leq \theta \leq 2\pi$ .

Ok. But when I read the result for $\cos\theta = k$, the interval was given $-\pi < \theta \leq \pi$ .

Now, I want to know what is the cause for the different intervals. Can't they be same? I want to post this but not getting any proper title. Can anyone please suggest me a good title which portrays my problem?

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I think I'd go along the lines of one of the following:

  • Codomains of inverse sine and cosine
  • Description of preimages of values of sine and cosine
  • Describing solutions to $\sin \theta = k$ and $\cos \theta = k$
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