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Exercises Trigonometry

Example 1 from Algebra and Trigonometry, 8.1 Graphs of the Sine and Cosine Functions

Identifying the Period of a Sine or Cosine Function

Determine the period of the function $f (x) = \sin (\frac{π}{6} x) .$

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 $y = A \sin (B x) .$
In the given equation, $B = \frac{π}{6},$ so the period will be

$\begin{array}{l} \begin{array}{l} P = \frac{2 π}{| B |} \end{array} \\ = \frac{2 π}{\frac{π}{6}} \\ = 2 π \cdot \frac{6}{π} \\ = 12 \end{array}$

Your turn

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

Determine the period of the function $g (x) = \cos (\frac{x}{3}) .$

How did it go?

PreviousEvaluating the Cosecant Using Technology Next Identifying the Amplitude of a Sine or Cosine Function

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.