A Ferris wheel has a diameter of 38 ft. The bottom of the Ferris wheel is 3 ft. off the ground and it makes one revolution every 30 seconds. After you board the Ferris wheel it takes you 14 seconds to get to the top. Write an equation for your height in feet, h , off the ground t seconds after you board.

h = 19 cos ⁡ ( π 15 ( x − 14 ) ) + 22 h\ =\ 19\cos\left(\frac{π}{15}\left(x-14\right)\right)+22 h = 1 9 cos ( 1 5 π ( x − 1 4 ) ) + 2 2

h = − 22 cos ⁡ ( 30 ( x − 14 ) ) + 19 h\ =\ -22\cos\left(30\left(x-14\right)\right)+19 h = − 2 2 cos ( 3 0 ( x − 1 4 ) ) + 1 9

h = − 19 sin ⁡ ( 30 ( x − 14 ) ) + 22 h\ =-19\sin\left(30\left(x-14\right)\right)+22 h = − 1 9 sin ( 3 0 ( x − 1 4 ) ) + 2 2

h = 22 sin ⁡ ( π 15 ( x − 14 ) ) + 19 h\ =\ 22\sin\left(\frac{π}{15}\left(x-14\right)\right)+19 h = 2 2 sin ( 1 5 π ( x − 1 4 ) ) + 1 9

Write an equation for graph shown.

y = − 4 cos ⁡ π x y=-4\cosπx y = − 4 cos π x

y = cos ⁡ 2 x + 4 y=\cos2x\ +\ 4 y = cos 2 x + 4

y = 4 sin ⁡ 2 x y=4\sin2x y = 4 sin 2 x

y = − sin ⁡ π x + 4 y=-\sinπx\ +\ 4 y = − sin π x + 4

y = sin ⁡ ( 8 π x + 4 π 3 ) y=\sin\left(8\pi x+\frac{4\pi}{3}\right) y = sin ( 8 π x + 3 4 π ) is equivalent to...

y = sin ⁡ 8 π ( x + 1 6 ) y=\sin8\pi\left(x+\frac{1}{6}\right) y = sin 8 π ( x + 6 1 )

y = sin ⁡ 8 π ( x + π 6 ) y=\sin8\pi\left(x+\frac{\pi}{6}\right) y = sin 8 π ( x + 6 π )

y = sin ⁡ 8 π ( x + 4 π 3 ) y=\sin8\pi\left(x+\frac{4\pi}{3}\right) y = sin 8 π ( x + 3 4 π )

y = sin ⁡ 8 π ( x + 32 π 3 ) y=\sin8\pi\left(x+\frac{32\pi}{3}\right) y = sin 8 π ( x + 3 3 2 π )

Which of these functions is different from the others?

f ( x ) = − 2 sin ⁡ ( 2 ( x − π 2 ) ) f\left(x\right)=-2\sin\left(2\left(x-\frac{π}{2}\right)\right) f ( x ) = − 2 sin ( 2 ( x − 2 π ) )

f ( x ) = 1 − 3 sin ⁡ ( 2 ( x − π 2 ) ) f\left(x\right)=1-3\sin\left(2\left(x-\frac{π}{2}\right)\right) f ( x ) = 1 − 3 sin ( 2 ( x − 2 π ) )

f ( x ) = 1 − 3 sin ⁡ ( 2 x − π ) f\left(x\right)=1-3\sin\left(2x-π\right) f ( x ) = 1 − 3 sin ( 2 x − π )

f ( x ) = 1 − 3 sin ⁡ ( 4 ( x 2 − π 4 ) ) f\left(x\right)=1-3\sin\left(4\left(\frac{x}{2}-\frac{π}{4}\right)\right) f ( x ) = 1 − 3 sin ( 4 ( 2 x − 4 π ) )

Which is equivalent to: y = sin ⁡ − 1 x y=\sin^{-1}x y = sin − 1 x ?

x = sin ⁡ y x=\sin y x = sin y where − π 2 ≤ y ≤ π 2 -\frac{π}{2}\le y\le\frac{π}{2} − 2 π ≤ y ≤ 2 π

x = sin ⁡ y x=\sin y x = sin y where − π 2 < x < π 2 -\frac{π}{2}<x<\frac{π}{2} − 2 π < x < 2 π

y = csc ⁡ x y=\csc x y = csc x where 0 ≤ x ≤ π 0\le x\leπ 0 ≤ x ≤ π

y = sec ⁡ x y=\sec x y = sec x where 0 < x < π 0<x<π 0 < x < π

Which is equivalent to: y = cos ⁡ − 1 x y=\cos^{-1}x y = cos − 1 x ?

x = cos ⁡ y x=\cos y x = cos y where 0 ≤ y ≤ π 0\le y\leπ 0 ≤ y ≤ π

y = sec ⁡ x y=\sec x y = sec x where − π 2 ≤ y ≤ π 2 -\frac{π}{2}\le y\le\frac{π}{2} − 2 π ≤ y ≤ 2 π

x = sec ⁡ y x=\sec y x = sec y where − π 2 < x < π 2 -\frac{π}{2}<x<\frac{π}{2} − 2 π < x < 2 π

y = cos ⁡ x y=\cos x y = cos x where 0 < x < π 0<x<π 0 < x < π

Which is NOT equivalent to: y = sec ⁡ − 1 x y=\sec^{-1}x y = sec − 1 x ?

y = 1 cos ⁡ x y=\frac{1}{\cos x} y = cos x 1 where 0 ≤ y ≤ π 0 ≤ y ≤ π

y = cos ⁡ − 1 ( 1 x ) y=\cos^{-1}\left(\frac{1}{x}\right) y = cos − 1 ( x 1 )

x = 1 cos ⁡ y x=\frac{1}{\cos y} x = cos y 1 where 0 ≤ y ≤ π 0\le y\leπ 0 ≤ y ≤ π

cos ⁡ y = 1 x \cos y=\frac{1}{x} cos y = x 1 where 0 ≤ y ≤ π 0\le y\leπ 0 ≤ y ≤ π

Which is NOT equivalent to: y = csc ⁡ − 1 x y=\csc^{-1}x y = csc − 1 x ?

y = 1 sin ⁡ x y=\frac{1}{\sin x} y = sin x 1 where − π 2 ≤ y ≤ π 2 − 2 π ≤ y ≤ 2 π

y = sin ⁡ − 1 ( 1 x ) y=\sin^{-1}\left(\frac{1}{x}\right) y = sin − 1 ( x 1 )

x = 1 sin ⁡ y x=\frac{1}{\sin y} x = sin y 1 where − π 2 ≤ y ≤ π 2 -\frac{π}{2}\le y\le\frac{π}{2} − 2 π ≤ y ≤ 2 π

sin ⁡ y = 1 x \sin y=\frac{1}{x} sin y = x 1 where − π 2 ≤ y ≤ π 2 − 2 π ≤ y ≤ 2 π

Find the secant of the angle whose terminal side passes through (5, –1).

26 5 \frac{\sqrt{26}}{5} 5 2 6 <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">

24 5 \frac{\sqrt{24}}{5} 5 2 4 <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">

− 26 -\sqrt{26} − 2 6 <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">

− 24 -\sqrt{24} − 2 4 <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 ⁡ θ = 5 6 \sin\theta=\frac{5}{6} sin θ = 6 5 and tan ⁡ θ < 0 \tan\theta<0 tan θ < 0 . Find cos ⁡ θ \cos\theta cos θ .

− 11 6 -\frac{\sqrt{11}}{6} − 6 1 1 <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 ⁡ θ = − 1 2 \tan\theta=-\frac{1}{2} tan θ = − 2 1 and sin ⁡ θ < 0 \sin\theta<0 sin θ < 0 . Find cos ⁡ θ \cos\theta cos θ .

2 5 5 \frac{2\sqrt{5}}{5} 5 2 5 <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">

− 5 2 -\frac{\sqrt{5}}{2} − 2 5 <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">

− 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">

sec ⁡ θ = 3 \sec\theta=3 sec θ = 3 and sin ⁡ θ > 0 \sin\theta>0 sin θ > 0 . Find tan ⁡ θ \tan\theta tan θ .

2 2 2\sqrt{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 5 2 \frac{2\sqrt{5}}{2} 2 2 5 <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">

− 5 2 -\frac{\sqrt{5}}{2} − 2 5 <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">

Precalc - Review for Term 2 Cumulative 2019-2020

Authored by Leah Burby

Mathematics

10th Grade - University

CCSS covered

Used 1+ times

Precalc - Review for Term 2 Cumulative 2019-2020

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

sec 3π/2

undefined

-1

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

cos 4π/3

-√3/2

√3/2

1/2

-1/2

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

cot 3π/4

-√2/2

-1

√2/2

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

sin 7π/6

1/2

-1/2

√3/2

-√3/2

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

tan (-π)

undefined

-1

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the range of angles for inverse cosine?

[0, π]

[0, 2π]

[-π/2, π/2]

[π/2, 3π/2]

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the range of angles for inverse sine?

[0, π]

[0, 2π]

[-π/2, π/2]

[π/2, 3π/2]

Tags

CCSS.HSF-BF.B.4D

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Precalc - Review for Term 2 Cumulative 2019-2020

sec 3π/2

cos 4π/3

cot 3π/4

sin 7π/6

tan (-π)

What is the range of angles for inverse cosine?

What is the range of angles for inverse sine?

What is the range of angles for inverse tangent?

tan^-1(-√(3))=

cos^-1(- √(3)/2) =

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Precalc - Review for Term 2 Cumulative 2019-2020

sec 3π/2

cos 4π/3

cot 3π/4

sin 7π/6

tan (-π)

What is the range of angles for inverse cosine?

What is the range of angles for inverse sine?

What is the range of angles for inverse tangent?

tan-1(-√(3))=

cos-1(- √(3)/2) =

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tan^-1(-√(3))=

cos^-1(- √(3)/2) =