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

− π 4 -\frac{\pi}{4} − 4 π

− π 2 -\frac{\pi}{2} − 2 π

sin ⁡ − 1 ( − 3 2 ) = \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)= sin − 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"> ) =

− π 3 -\frac{\pi}{3} − 3 π

− π 4 -\frac{\pi}{4} − 4 π

− π 2 -\frac{\pi}{2} − 2 π

cos ⁡ − 1 ( sin ⁡ ( π 6 ) ) = \cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)= cos − 1 ( sin ( 6 π ) ) =

− π 4 -\frac{\pi}{4} − 4 π

− π 3 -\frac{\pi}{3} − 3 π

− π 2 -\frac{\pi}{2} − 2 π

cos ⁡ ( cos ⁡ − 1 ( 2 2 ) ) = \cos\left(\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)\right)= cos ( cos − 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"> ) ) =

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">

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">

sin ⁡ − 1 ( tan ⁡ ( π ) ) = \sin^{-1}\left(\tan\left(\pi\right)\right)= sin − 1 ( tan ( 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">

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">

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="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">

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

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">

− 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">

tan ⁡ − 1 ( 0 ) = \tan^{-1}\left(0\right)= tan − 1 ( 0 ) =

− π 6 -\frac{\pi}{6} − 6 π

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

tan ⁡ − 1 ( cot ⁡ ( π 4 ) ) = \tan^{-1}\left(\cot\left(\frac{\pi}{4}\right)\right)= tan − 1 ( cot ( 4 π ) ) =

− π 4 -\frac{\pi}{4} − 4 π

cos ⁡ − 1 ( sin ⁡ ( 5 π 3 ) ) = \cos^{-1}\left(\sin\left(\frac{5\pi}{3}\right)\right)= cos − 1 ( sin ( 3 5 π ) ) =

− π 6 -\frac{\pi}{6} − 6 π

− π 4 -\frac{\pi}{4} − 4 π

14 Unit Circle with Inverse & Composition (No Calc)

Authored by Paula Schute

Mathematics

10th - 12th Grade

CCSS covered

Used 102+ times

14 Unit Circle with Inverse & Composition (No Calc)

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15 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\tan^{-1}\left(\sqrt{3}\right)=$

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\tan^{-1}\left(-1\right)=$

$\frac{\pi}{4}$

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

$\frac{\pi}{3}$

$-\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\frac{\pi}{4}$

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

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

$-\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)=$

$\frac{\pi}{3}$

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

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

$-\frac{\pi}{2}$

$0$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

$-1$

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

$0$

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

$-1$

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

$0$

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos\left(\tan^{-1}\left(-1\right)\right)=$

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

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

$-1$

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

$0$

Tags

CCSS.HSF-BF.B.4A

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

$-1$

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

$0$

Tags

CCSS.HSF.TF.B.7

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14 Unit Circle with Inverse & Composition (No Calc)

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

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

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

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

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

cos⁡−1(sin⁡(π6))=\cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)=cos−1(sin(6π​))=

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

sin⁡−1(tan⁡(π))=\sin^{-1}\left(\tan\left(\pi\right)\right)=sin−1(tan(π))=

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

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

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

$\tan^{-1}\left(\sqrt{3}\right)=$

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

$\tan^{-1}\left(-1\right)=$

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

$\cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)=$

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

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

$\cos\left(\tan^{-1}\left(-1\right)\right)=$

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