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Exercises Trigonometry

Example 4 from Algebra and Trigonometry, 8.1 Graphs of the Sine and Cosine Functions

Identifying the Vertical Shift of a Function

Determine the direction and magnitude of the vertical shift for $f (x) = \cos (x) - 3.$

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
Let’s begin by comparing the equation to the general form $y = A \cos (B x - C) + D .$
In the given equation, $D = −3$ so the shift is 3 units downward.

Your turn

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

Determine the direction and magnitude of the vertical shift for $f (x) = 3 \sin (x) + 2.$

How did it go?

PreviousIdentifying the Phase Shift of a Function Next Identifying the Variations of a Sinusoidal Function from an Equation

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 8.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.