Unit 7, Lesson 14
Amplitude and Midline
Algebra 2
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Here is a graph of the equation \(y = 2\sin(\theta) - 3\).
A graph. Horizontal axis, theta, scale negative 2 pi to pi by pi over 2. Vertical axis, y, scale negative 5 to 1. The curve passes through the points negative 3 pi over 2 comma negative 1, negative pi comma negative 3, negative pi over 2 comma negative 5, 0 comma negative 3, pi over 2 comma negative 1, pi comma negative 3, 3 pi over 2 comma negative 5.
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 point \(P\), \(f(\theta)\), in feet.
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
The picture shows two points, \(P\) and \(Q\), on the unit circle.
Explain why the tangent of \(P\) and \(Q\) is 2.
A circle with center at the origin of an x y plane with grid. The circle has a diameter of 4 units. The point P lies on the outside of the circle, in the first quadrant, and is closer to the y axis than the x axis. Point Q lies on the outside of the circle, in the third quadrant, and is closer to the y axis than the x axis. A line passes through points P and Q.