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

[ − 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 ]

Domain 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 )

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

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

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

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

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

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

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

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

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 ]

tan ⁡ − 1 x + cot ⁡ − 1 x = π / 2 w h e n \tan^{-1}x+\cot^{-1}x=π/2\ when tan − 1 x + cot − 1 x = π / 2 w h e n

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

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

F o r x ∈ [ − 1 , 1 ] , sin ⁡ − 1 ( − x ) = For\ \ x∈[-1,1],\ \sin^{-1}(-x)= F o r x ∈ [ − 1 , 1 ] , sin − 1 ( − x ) =

– sin ⁡ − 1 ( x ) , –\sin^{-1}(x),\ \ \ – sin − 1 ( x ) ,

π − sin ⁡ − 1 ( x ) , \pi-\sin^{-1}(x),\ \ \ π − sin − 1 ( x ) ,

π + sin ⁡ − 1 x \pi\ +\ \sin^{-1}x π + sin − 1 x

sin ⁡ − 1 x \sin^{-1}x sin − 1 x

T h e v a l u e o f sin ⁡ − 1 ( 1 2 ) i s The\ value\ of\ \sin^{-1}\left(\frac{1}{2}\right)\ is T h e v a l u e o f sin − 1 ( 2 1 ) i s

− π 3 -\frac{\pi}{3} − 3 π

− π 6 -\frac{\pi}{6} − 6 π

T h e v a l u e o f sin ⁡ − 1 ( − 1 2 ) i s The\ value\ of\ \sin^{-1}\left(-\frac{1}{2}\right)\ is T h e v a l u e o f sin − 1 ( − 2 1 ) i s

− π 6 -\frac{\pi}{6} − 6 π

− π 3 -\frac{\pi}{3} − 3 π

T h e v a l u e o f cos ⁡ − 1 ( 3 2 ) i s The\ value\ of\ \ \cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\ is T h e v a l u e o f 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"> ) i s

− π 3 -\frac{\pi}{3} − 3 π

− π 6 -\frac{\pi}{6} − 6 π

T h e v a l u e o f cos ⁡ − 1 ( − 3 2 ) i s The\ value\ of\ \ \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\ is T h e v a l u e o f 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"> ) i s

− 5 π 6 -\frac{5\pi}{6} − 6 5 π

− π 6 -\frac{\pi}{6} − 6 π

cos ⁡ − 1 cos ⁡ 13 π 6 = \cos^{-1}\cos\ \frac{13\pi}{6}\ = cos − 1 cos 6 1 3 π =

− π 6 -\frac{\pi}{6} − 6 π

13 π 6 \frac{13\pi}{6} 6 1 3 π

tan ⁡ − 1 tan ⁡ 9 π 8 \tan^{-1}\tan\ \frac{9\pi}{8} tan − 1 tan 8 9 π

− π 8 -\frac{\pi}{8} − 8 π

The principal value branch of sec ⁡ − 1 x \sec^{-1}x sec − 1 x is

[ 0 , π ] − { π 2 } \left[0,\pi\right]-\left\{\frac{\pi}{2}\right\} [ 0 , π ] − { 2 π }

\left[-\frac{\pi}{2},\frac{\pi}{2}\right] [ − 2 π , 2 π ] -\left\{0\right\} − { 0 }

( 0 , π ) − { π 2 } \left(0,\pi\right)-\left\{\frac{\pi}{2}\right\} ( 0 , π ) − { 2 π }

MCQ on Inverse Trigonometric functions

Authored by Pratima Nayak

Mathematics

11th - 12th Grade

CCSS covered

Used 197+ times

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20 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 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

30 sec • 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

30 sec • 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

30 sec • 1 pt

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

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

$\left(0,\pi\right)$

MULTIPLE CHOICE QUESTION

30 sec • 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

30 sec • 1 pt

$The\ value\ of\ \sin^{-1}x+\cos^{-1}x,\ \ \ \ \ x∈[-1,1]$

$=1$

$=\frac{\pi}{2}$

$=\pi$

$=0$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\tan^{-1}x+\cot^{-1}x=π/2\ when$

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

$x\in R$

$x\in+R$

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

Tags

CCSS.HSF.TF.B.7

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

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MCQ on Inverse Trigonometric functions

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

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

Domain of function cot⁡−1x is\cot^{-1}x\ iscot−1x is

Range of function cot⁡−1x is\cot^{-1}x\ iscot−1x is

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

The value of sin⁡−1x+cos⁡−1x, x∈[−1,1]The\ value\ of\ \sin^{-1}x+\cos^{-1}x,\ \ \ \ \ x∈[-1,1]The value of sin−1x+cos−1x, x∈[−1,1]

tan⁡−1x+cot⁡−1x=π/2 when\tan^{-1}x+\cot^{-1}x=π/2\ whentan−1x+cot−1x=π/2 when

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

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$\tan^{-1}x+\cot^{-1}x=π/2\ when$