Why isn't $\mathrm{arctan}\theta =\frac{\mathrm{arcsin}\theta}{\mathrm{arccos}\theta}$?

Brunton39
2022-07-01
Answered

Why isn't $\mathrm{arctan}\theta =\frac{\mathrm{arcsin}\theta}{\mathrm{arccos}\theta}$?

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drumette824ed

Answered 2022-07-02
Author has **19** answers

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.

However $\frac{\mathrm{arcsin}x}{\mathrm{arccos}x}$ is unbounded as $x\to \pi /2$, so this can not be a value of arctan.

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