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Here is a graph of a trigonometric function. Which equation could define this function?
\(y = 1.5\sin(x) - 4\)
\(y = 1.5\cos(x) - 4\)
\(y = \text-4\sin(1.5x)\)
\(y = \text-4\cos(1.5x)\)
Select all the functions that have period \(\pi\).
\(y = \cos\left(\frac{x}{2}\right)\)
\(y = \sin\left(\frac{x}{2}\right)\)
\(y = \cos(x)\)
\(y = \cos(2x)\)
\(y = \sin(2x)\)
Sketch a graph of \(a(\theta) = \cos(3\theta)\).
Compare the graph of \(a\) to the graph of \(b(\theta)=\cos(\theta)\). How are the two graphs alike? How are they different?
The functions, \(f\) and \(g\), are given by \(f(x) = \cos(x)\) and \(g(x) = \cos(5x)\). How are the graphs of \(f\) and \(g\) related?
Here is a point at the tip of a windmill blade. The center of the windmill is 6 feet off the ground and the blades are 1.5 feet long.
Write an equation giving the height, \(h\), of point \(P\) after the windmill blade rotates by an angle of \(a\). Point \(P\) is currently rotated \(\frac{\pi}{4}\) radian from the point directly to the right of the center of the windmill.
The coordinates of \(P\) are \((1,0)\).
A Ferris wheel has a radius of 95 feet and its center is 105 feet above the ground. Which statement is true about a point on the Ferris wheel as it goes around in a circle?
It is 85 feet off the ground once in Quadrant I and once in Quadrant II.
It is 85 feet off the ground once in Quadrant II and once in Quadrant III.
It is 85 feet off the ground once in Quadrant III and once in Quadrant IV.
It is 85 feet off the ground once in Quadrant IV and once in Quadrant I.