cos ⁡ − 1 ( − 1 ) \cos^{-1}\left(-1\right) cos − 1 ( − 1 )

− π 2 -\frac{\pi}{2} − 2 π

sin ⁡ − 1 ( − 1 ) \sin^{-1}\left(-1\right) sin − 1 ( − 1 )

− π 2 -\frac{\pi}{2} − 2 π

− π 4 -\frac{\pi}{4} − 4 π

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 6 -\frac{\pi}{6} − 6 π

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

tan ⁡ ( tan ⁡ − 1 ( 3 ) ) \tan\left(\tan^{-1}\left(\sqrt{3}\right)\right) tan ( tan − 1 ( 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" /> ) )

3 \sqrt{3} 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" />

− 3 -\sqrt{3} − 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" />

cos ⁡ − 1 ( cos ⁡ ( 2 π 3 ) ) \cos^{-1}\left(\cos\left(\frac{2\pi}{3}\right)\right) cos − 1 ( cos ( 3 2 π ) )

− 2 π 3 -\frac{2\pi}{3} − 3 2 π

sin ⁡ − 1 ( sin ⁡ ( 3 π 4 ) ) \sin^{-1}\left(\sin\left(\frac{3\pi}{4}\right)\right) sin − 1 ( sin ( 4 3 π ) )

− π 4 -\frac{\pi}{4} − 4 π

tan ⁡ − 1 ( − 1 ) \tan^{-1}\left(-1\right) tan − 1 ( − 1 )

− π 4 -\frac{\pi}{4} − 4 π

cos ⁡ ( sin ⁡ − 1 ( 1 2 ) ) \cos\left(\sin^{-1}\left(\frac{1}{2}\right)\right) cos ( sin − 1 ( 2 1 ) )

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

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

cos ⁡ ( tan ⁡ − 1 ( − 1 ) ) \cos\left(\tan^{-1}\left(-1\right)\right) cos ( tan − 1 ( − 1 ) )

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

− 2 2 -\frac{\sqrt{2}}{2} − 2 2 <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" />

9.1 Inverse Trig Functions

Authored by D. Vuong

Mathematics

11th - 12th Grade

CCSS covered

Used 73+ times

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18 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\sin^{-1}\left(1\right)$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

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

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

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

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

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

$\frac{7\pi}{6}$

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

Tags

CCSS.HSF.TF.B.7

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9.1 Inverse Trig Functions

sin⁡−1(32)\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)sin−1(23​​)

cos⁡−1(22)\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)cos−1(22​​)

sin⁡−1(1)\sin^{-1}\left(1\right)sin−1(1)

tan⁡−1(3)\tan^{-1}\left(\sqrt{3}\right)tan−1(3​)

cos⁡−1(−1)\cos^{-1}\left(-1\right)cos−1(−1)

tan⁡−1(1)\tan^{-1}\left(1\right)tan−1(1)

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

sin⁡−1(−1)\sin^{-1}\left(-1\right)sin−1(−1)

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

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

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$\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$

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$\sin^{-1}\left(-1\right)$

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

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