Find the exact value of sin ⁡ − 1 ( − 2 2 ) \sin^{-1}\left(-\frac{\sqrt{2}}{2}\right) sin − 1 ( − 2 2 <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"> ) .

− π 4 -\frac{\pi}{4} − 4 π

Find the exact 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 4 -\frac{\pi}{4} − 4 π

Find the exact value of sin ⁡ ( tan ⁡ − 1 ( 3 ) ) \sin\left(\tan^{-1}\left(\sqrt{3}\right)\right) sin ( tan − 1 ( 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"> ) ) .

3 2 \frac{\sqrt{3}}{2} 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">

2 2 \frac{\sqrt{2}}{2} 2 2 <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">

− 3 2 -\frac{\sqrt{3}}{2} − 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">

− 2 2 -\frac{\sqrt{2}}{2} − 2 2 <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">

Find the exact value of cos ⁡ − 1 ( tan ⁡ π 4 ) \cos^{-1}\left(\tan\ \frac{\pi}{4}\right) cos − 1 ( tan 4 π ) .

2 2 \frac{\sqrt{2}}{2} 2 2 <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">

− 2 2 -\frac{\sqrt{2}}{2} − 2 2 <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">

Find the exact value of tan ⁡ − 1 ( tan ⁡ 3 π 4 ) \tan^{-1}\left(\tan\ \frac{3\pi}{4}\right) tan − 1 ( tan 4 3 π ) .

− π 4 -\frac{\pi}{4} − 4 π

− π 3 -\frac{\pi}{3} − 3 π

Inverse Trigonometric Functions Quiz

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Math

Trigonometry

Inverse Trigonometric Functions

Authored by Jose C

Mathematics

11th - 12th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which can be a restriction for the domain of y = sin x so the inverse sine can be a function?

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

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

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

$\left[0,\ 2\pi\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which can be a restriction for the domain of y = cos x so the inverse cosine can be a function?

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

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

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

$\left[0,\ 2\pi\right]$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ .

$\frac{\pi}{6}$

$\frac{3\pi}{4}$

$\frac{2\pi}{3}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$ .

$\frac{\pi}{6}$

$\frac{3\pi}{4}$

$\frac{2\pi}{3}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ .

$\frac{\pi}{6}$

$-\frac{\pi}{4}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\sin^{-1}\left(-\frac{1}{2}\right)$ .

$\frac{\pi}{6}$

$-\frac{\pi}{4}$

$\frac{\pi}{4}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)$ .

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$

$-\frac{\sqrt{3}}{2}$

$-\frac{\sqrt{2}}{2}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\cos^{-1}\left(\tan\ \frac{\pi}{4}\right)$ .

$\frac{\sqrt{2}}{2}$

$-\frac{\sqrt{2}}{2}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of $\tan^{-1}\left(\tan\ \frac{3\pi}{4}\right)$ .

$\frac{\pi}{4}$

$-\frac{\pi}{4}$

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

$\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

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Inverse Trigonometric Functions

Which can be a restriction for the domain of y = sin x so the inverse sine can be a function?

Which can be a restriction for the domain of y = cos x so the inverse cosine can be a function?

Find the exact value of cos⁡−1(−32)\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)cos−1(−23​​) .

Find the exact value of tan⁡−1(32)\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)tan−1(23​​) .

Find the exact value of sin⁡−1(−22)\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)sin−1(−22​​) .

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

Find the exact value of sin⁡(tan⁡−1(3))\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)sin(tan−1(3​)) .

Find the exact value of cos⁡−1(tan⁡ π4)\cos^{-1}\left(\tan\ \frac{\pi}{4}\right)cos−1(tan 4π​) .

Find the exact value of tan⁡−1(tan⁡ 3π4)\tan^{-1}\left(\tan\ \frac{3\pi}{4}\right)tan−1(tan 43π​) .

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Discover more resources for Mathematics

Find the exact value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ .

Find the exact value of $\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$ .

Find the exact value of $\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ .

Find the exact value of $\sin^{-1}\left(-\frac{1}{2}\right)$ .

Find the exact value of $\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)$ .

Find the exact value of $\cos^{-1}\left(\tan\ \frac{\pi}{4}\right)$ .

Find the exact value of $\tan^{-1}\left(\tan\ \frac{3\pi}{4}\right)$ .