# Why isn't arctan &#x2061;<!-- ⁡ --> &#x03B8;<!-- θ --> = arcsin

Why isn't $\mathrm{arctan}\theta =\frac{\mathrm{arcsin}\theta }{\mathrm{arccos}\theta }$?
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drumette824ed
For one thing, the principal value of arctan is from 0 to π on Monday, Wednesday, and Friday, and from $-\pi /2$ to $\pi /2$ on Tuesday, Thursday, and Saturday.
However $\frac{\mathrm{arcsin}x}{\mathrm{arccos}x}$ is unbounded as $x\to \pi /2$, so this can not be a value of arctan.