Example 11 from Algebra and Trigonometry, 8.1 Graphs of the Sine and Cosine Functions

Finding the Vertical Component of Circular Motion

A point rotates around a circle of radius 3 centered at the origin. Sketch a graph of the y-coordinate of the point as a function of the angle of rotation.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Recall that, for a point on a circle of radius r, the y-coordinate of the point is $y = r \sin (x),$ so in this case, we get the equation $y (x) = 3 \sin (x) .$ The constant 3 causes a vertical stretch of the y-values of the function by a factor of 3, which we can see in the graph in Figure 22.

Figure 22

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

What is the amplitude of the function $f (x) = 7 \cos (x) ?$ Sketch a graph of this function.

How did it go?

Solution

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Solution

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