Back to Restrict domain for inverse trig functions — Problem 2 · Task Set 73

HSF.TF.B.6 Tutor Intake -- Inverse Trig Domain Restrictions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-tf-b-6

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Concepts

Which row correctly lists all three standard restricted domains used to
define $\arcsin$ , $\arccos$ , and $\arctan$ ?

$\arcsin$ : $\left[-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right]$ ;
$\arccos$ : $[0, \pi]$ ;
$\arctan$ : $\left(-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right)$

$\arcsin$ : $[0, \pi]$ ;
$\arccos$ : $\left[-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right]$ ;
$\arctan$ : $\left(-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right)$

$\arcsin$ : $\left[-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right]$ ;
$\arccos$ : $\left[-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right]$ ;
$\arctan$ : $(0, \pi)$

$\arcsin$ : $[-1, 1]$ ;
$\arccos$ : $[-1, 1]$ ;
$\arctan$ : $(-\infty, \infty)$