Find the exact value of the expression: tan ⁡ ( sin ⁡ − 1 ( − 1 2 ) ) \tan\left(\sin^{-1}\left(-\frac{1}{2}\right)\right) tan ( sin − 1 ( − 2 1 ) )

− 3 3 -\frac{\sqrt{3}}{3} − 3 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 \sqrt{3} 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 3 \frac{\sqrt{3}}{3} 3 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 -\sqrt{3} − 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 ⁡ − 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

Which of the following has an answer that is different from the rest?

C o s − 1 ( cos ⁡ ( 4 π 3 ) ) Cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right) C o s − 1 ( cos ( 3 4 π ) )

S i n − 1 ( sin ⁡ ( 2 π 3 ) ) Sin^{-1}\left(\sin\left(\frac{2\pi}{3}\right)\right) S i n − 1 ( sin ( 3 2 π ) )

S i n − 1 ( sin ⁡ ( π 3 ) ) Sin^{-1}\left(\sin\left(\frac{\pi}{3}\right)\right) S i n − 1 ( sin ( 3 π ) )

C o s − 1 ( cos ⁡ ( 5 π 3 ) ) Cos^{-1}\left(\cos\left(\frac{5\pi}{3}\right)\right) C o s − 1 ( cos ( 3 5 π ) )

Which of the angles below fall in the range [ 0 , π ] \left[0,\ \pi\right] [ 0 , π ] ? (Check all that apply)

− π 2 -\frac{\pi}{2} − 2 π

Which of the angles below fall in the range [ − π 2 , π 2 ] \left[-\frac{\pi}{2},\ \frac{\pi}{2}\right] [ − 2 π , 2 π ] ? (Check all that apply)

− π 6 -\frac{\pi}{6} − 6 π

− π 2 -\frac{\pi}{2} − 2 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">

4.1b Composition of Trig Fxns

Authored by Erin Inman

Mathematics

11th - 12th Grade

CCSS covered

Used 37+ times

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20 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

$\sqrt{3}$

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

$-\sqrt{3}$

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

Tags

CCSS.HSF.TF.C.8

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of the expression: tan^-1(sin π)

-1

undefined

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the exact value of the expression: $\tan\left(\sin^{-1}\left(1\right)\right)$

undefined

$\frac{1}{2}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

$0$

$\pi$

$\frac{\pi}{4}$

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

Tags

CCSS.HSF.TF.A.2

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

cos^-1(sin(-π/4))

3π/4

π/2

-π/4

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

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

$\frac{\pi}{4}$

$\frac{\pi}{3}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)$

$\frac{-1}{2}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

$\frac{1}{2}$

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

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

$0$

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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4.1b Composition of Trig Fxns

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

Find the exact value of the expression: tan-1(sin π)

Find the exact value of the expression: tan⁡(sin⁡−1(1))\tan\left(\sin^{-1}\left(1\right)\right)tan(sin−1(1))

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

sin-1(cos(5π/6))

cos-1(sin(-π/4))

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

cos⁡−1(cos⁡(4π3))\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)cos−1(cos(34π​))

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

Find the exact value of the expression: tan^-1(sin π)

Find the exact value of the expression: $\tan\left(\sin^{-1}\left(1\right)\right)$

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

sin^-1(cos(5π/6))

cos^-1(sin(-π/4))

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

$\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)$

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

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