Domain of function sin ⁡ − 1 x i s \sin^{-1}x\ is sin − 1 x i s

[ − 1 , 1 ] \left[-1,1\right] [ − 1 , 1 ]

[ − π 2 , π 2 ] \left[-\frac{\pi}{2},\frac{\pi}{2}\right] [ − 2 π , 2 π ]

( − π 2 , π 2 ) \left(-\frac{\pi}{2},\frac{\pi}{2}\right) ( − 2 π , 2 π )

( − 1 , 1 ) \left(-1,1\right) ( − 1 , 1 )

Domain of function cos ⁡ − 1 x i s \cos^{-1}x\ is cos − 1 x i s

[ − 1 , 1 ] \left[-1,1\right] [ − 1 , 1 ]

[ − π 2 , π 2 ] \left[-\frac{\pi}{2},\frac{\pi}{2}\right] [ − 2 π , 2 π ]

( − π 2 , π 2 ) \left(-\frac{\pi}{2},\frac{\pi}{2}\right) ( − 2 π , 2 π )

( − 1 , 1 ) \left(-1,1\right) ( − 1 , 1 )

Range of function sin ⁡ − 1 x i s \sin^{-1}x\ is sin − 1 x i s

[ − π 2 , π 2 ] \left[-\frac{\pi}{2},\frac{\pi}{2}\right] [ − 2 π , 2 π ]

( − π 2 , π 2 ) \left(-\frac{\pi}{2},\frac{\pi}{2}\right) ( − 2 π , 2 π )

( − 1 , 1 ) \left(-1,1\right) ( − 1 , 1 )

[ − 1 , 1 ] \left[-1,1\right] [ − 1 , 1 ]

Range of function cos ⁡ − 1 x i s \cos^{-1}x\ is cos − 1 x i s

[ 0 , π ] \left[0,\ \pi\right] [ 0 , π ]

( − π 2 , π 2 ) \left(-\frac{\pi}{2},\frac{\pi}{2}\right) ( − 2 π , 2 π )

( − 1 , 1 ) \left(-1,1\right) ( − 1 , 1 )

[ − 1 , 1 ] \left[-1,1\right] [ − 1 , 1 ]

Range of function tan ⁡ − 1 x i s \tan^{-1}x\ is tan − 1 x i s

( − π 2 , π 2 ) \left(-\frac{\pi}{2},\frac{\pi}{2}\right) ( − 2 π , 2 π )

R − { π 2 } R-\left\{\frac{\pi}{2}\right\} R − { 2 π }

[ − π 2 , π 2 ] \left[-\frac{\pi}{2},\frac{\pi}{2}\right] [ − 2 π , 2 π ]

The value of sin ⁡ − 1 ( − 1 2 ) \sin^{-1}\left(-\frac{1}{2}\right)\ sin − 1 ( − 2 1 )

− π 6 -\frac{\pi}{6} − 6 π

− π 3 -\frac{\pi}{3} − 3 π

The value of cos ⁡ − 1 ( − 3 2 ) \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\ cos − 1 ( − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ) is

− 5 π 6 -\frac{5\pi}{6} − 6 5 π

− π 6 -\frac{\pi}{6} − 6 π

Find the exact value of cos ⁡ − 1 ( 3 2 ) \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) cos − 1 ( 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> )

− π 3 -\frac{\pi}{3} − 3 π

− π 6 -\frac{\pi}{6} − 6 π

Find the exact value of sec ⁡ − 1 ( − 2 ) \sec^{-1}\left(-2\right) sec − 1 ( − 2 )

− π 3 -\frac{\pi}{3} − 3 π

− 2 π 3 -\frac{2\pi}{3} − 3 2 π

cot ⁡ − 1 [ cot ⁡ ( − 9 π 4 ) ] \cot^{-1}\left[\cot\left(\frac{-9\pi}{4}\right)\right] cot − 1 [ cot ( 4 − 9 π ) ]

− π 4 \frac{-\pi}{4} 4 − π

− 3 π 4 \frac{-3\pi}{4} 4 − 3 π

1. The value of cos ⁡ − 1 ( cos ⁡ 7 π 6 ) \cos^{-1\ }\left(\cos\ \frac{7\pi}{6}\right) cos − 1 ( cos 6 7 π ) is

− π 6 -\frac{\pi}{6} − 6 π

Inverse Trigonometric Functions

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Practice Problem

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Hard

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CCSS

HSF.TF.B.7, HSF-BF.B.4D, HSF.TF.C.8

Standards-aligned

Lum Azeh

Used 80+ times

FREE Resource

30 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Domain of function $\sin^{-1}x\ is$

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\left(-1,1\right)$

$\left[-1,1\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Domain of function $\cos^{-1}x\ is$

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\left(-1,1\right)$

$\left[-1,1\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Range of function $\sin^{-1}x\ is$

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\left(-1,1\right)$

$\left[-1,1\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Range of function $\cos^{-1}x\ is$

$\left[0,\ \pi\right]$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\left(-1,1\right)$

$\left[-1,1\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Range of function $\tan^{-1}x\ is$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$R-\left\{\frac{\pi}{2}\right\}$

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

$-\frac{\pi}{3}$

$-\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

$\frac{5\pi}{6}$

$-\frac{5\pi}{6}$

$\frac{\pi}{6}$

$-\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

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Domain of function sin⁡−1x is\sin^{-1}x\ issin−1x is

Domain of function cos⁡−1x is\cos^{-1}x\ iscos−1x is

Range of function sin⁡−1x is\sin^{-1}x\ issin−1x is

Range of function cos⁡−1x is\cos^{-1}x\ iscos−1x is

Range of function tan⁡−1x is\tan^{-1}x\ istan−1x is

The value of sin⁡−1(−12) \sin^{-1}\left(-\frac{1}{2}\right)\ sin−1(−21​)

The value of cos⁡−1(−32) \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\ cos−1(−23​​) is

tan(sin-1(-1/2))

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Domain of function $\sin^{-1}x\ is$

Domain of function $\cos^{-1}x\ is$

Range of function $\sin^{-1}x\ is$

Range of function $\cos^{-1}x\ is$

Range of function $\tan^{-1}x\ is$

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

tan(sin^-1(-1/2))