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="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">

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

cos ⁡ − 1 ( cos ⁡ ( 7 π 4 ) ) \cos^{-1}\left(\cos\left(\frac{7\pi}{4}\right)\right) cos − 1 ( cos ( 4 7 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">

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 ⁡ ( sin ⁡ − 1 ( − 3 2 ) ) \cos\left(\sin^{-1}\left(\frac{-\sqrt{3}}{2}\right)\right) cos ( 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 6 \frac{-\pi}{6} 6 − π

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

Inverse Trig Compositions

Authored by Dustin Sharpe

Mathematics

9th - 12th Grade

CCSS covered

Used 77+ times

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12 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

sin(cos^-1(0))=

π/2

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

sin^-1(cos(5π/6))

-π/4

π/4

-π/3

π/6

Tags

CCSS.HSF.TF.B.7

CCSS.HSF.TF.A.3

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\frac{1}{2}$

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

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

$0$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)$

$\frac{1}{2}$

$\frac{-1}{2}$

$\frac{\pi}{6}$

$60^o$

Tags

CCSS.HSF.TF.B.7

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Inverse Trig Compositions

sin(cos-1(0))=

sin-1(cos(5π/6))

cos-1(sin(-π/4))

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

sin⁡−1(cos⁡(π4))\sin^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)sin−1(cos(4π​))

cos⁡−1(cos⁡(7π4))\cos^{-1}\left(\cos\left(\frac{7\pi}{4}\right)\right)cos−1(cos(47π​))

sin⁡−1(cos⁡(π3))\sin^{-1}\left(\cos\left(\frac{\pi}{3}\right)\right)sin−1(cos(3π​))

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

sin⁡−1(sin⁡(5π6))\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)sin−1(sin(65π​))

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sin(cos^-1(0))=

sin^-1(cos(5π/6))

cos^-1(sin(-π/4))

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

$\sin^{-1}\left(\cos\left(\frac{\pi}{4}\right)\right)$

$\cos^{-1}\left(\cos\left(\frac{7\pi}{4}\right)\right)$

$\sin^{-1}\left(\cos\left(\frac{\pi}{3}\right)\right)$

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

$\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)$