Illustrative Math - Algebra 2 - Unit 6 - Lesson 18

The vertical position, in feet, of the point P on a windmill is represented by y=5sin(\frac{2\pi t}{3})+20, where t  is the number of seconds after the windmill started turning at a constant speed. Select all the true statements.

• The windmill blades are 5 feet long.
• The windmill blades make 5 revolutions per second.
• The midline for the graph of the equation is 20.
• The windmill makes one revolution every 3 seconds.
• The windmill makes 3 revolutions per second.

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F.IF.7.e

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N.Q.1

A seat on a Ferris wheel travels 250\pi feet in one full revolution. How many feet is the carriage from the center of the Ferris wheel?

• \frac{125}{\pi}
• \frac{250}{\pi}
• 125
• 250

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F.IF.7.e

F.TF.5

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N.Q.1

A \frac{\pi}{2} radian rotation takes a point D on the unit circle to a point E. Which other radian rotation also takes point D to point E?

• \frac{3\pi}{2}
• \frac{4\pi}{2}
• \frac{5\pi}{2}
• \frac{7\pi}{2}

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F.IF.7.e

F.TF.5

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G.C.5

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N.Q.1

A windmill blade spins in a counterclockwise direction, making one full revolution every 5 seconds. Which statements are true? Select all that apply.

• After 15 seconds, the point W will be in its starting position.
• After \frac{1}{5} of a second, the point W will be in its starting position.
• In 1 second, the point W travels through an angle of \frac{1}{5}.
• The position of W repeats every 5 seconds.
• The position of W repeats every 10 seconds.

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F.IF.7.e

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G.C.5

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N.Q.1

Here is the graph of a trigonometric function. Which equation has this graph?

• y=-2sin(2x)
• y=2sin(2\pi(x+\frac{1}{4}))
• y=2sin(2\pi(x-\frac{1}{4}))
• y=2sin(2\pi(x+\frac{\pi}{4}))

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F.IF.7.e

F.TF.5

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G.C.5

F.BF.1.a

F.TF.1

N.Q.1