Lesson 13
Amplitude and Midline
Problem 1
For each trigonometric function, indicate the amplitude and midline.
- \(y = 2\sin(\theta)\)
- \(y = \cos(\theta) - 5\)
- \(y= 1.4 \sin(\theta) + 3.5\)
Solution
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Problem 2
Here is a graph of the equation \(y = 2\sin(\theta) - 3\).
- Indicate the midline on the graph.
- Use the graph to find the amplitude of this sine equation.
Solution
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Problem 3
Select all trigonometric functions with an amplitude of 3.
\(y = 3\sin(\theta) -1\)
\(y = \sin(\theta) + 3\)
\(y = 3\cos(\theta) + 2\)
\(y = \cos(\theta) - 3\)
\(y = 3\sin(\theta)\)
\(y = \cos(\theta - 3)\)
Solution
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Problem 4
The center of a windmill is 20 feet off the ground and the blades are 10 feet long.
rotation angle of windmill |
vertical position of \(P\) in feet |
---|---|
\(\frac{\pi}{6}\) | |
\(\frac{\pi}{3}\) | |
\(\frac{\pi}{2}\) | |
\(\pi\) | |
\(\frac{3\pi}{2}\) |
-
Fill out the table showing the vertical position of \(P\) after the windmill has rotated through the given angle.
-
Write an equation for the function \(f\) that describes the relationship between the angle of rotation \(\theta\) and the vertical position of the point \(P\), \(f(\theta)\), in feet.
Solution
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Problem 5
The measure of angle \(\theta\), in radians, satisfies \(\sin(\theta) < 0\). If \(\theta\) is between 0 and \(2\pi\) what can you say about the measure of \(\theta\)?
Solution
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(From Unit 6, Lesson 9.)Problem 6
Which rotations, with center \(O\), take \(P\) to \(Q\)? Select all that apply.
\(\frac{3\pi}{4}\) radians
\(\frac{15\pi}{4}\) radians
\(\frac{7\pi}{4}\) radians
\(\frac{11\pi}{4}\) radians
\(\frac{23\pi}{4}\) radians
Solution
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(From Unit 6, Lesson 10.)Problem 7
The picture shows two points \(P\) and \(Q\) on the unit circle.
Explain why the tangent of \(P\) and \(Q\) is 2.
Solution
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(From Unit 6, Lesson 12.)