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Sketching a Compressed Tangent · Physics Playground

Exercises Trigonometry

Example 1 from Algebra and Trigonometry, 8.2 Graphs of the Other Trigonometric Functions

Sketching a Compressed Tangent

Sketch a graph of one period of the function $y = 0.5 \tan (\frac{π}{2} x) .$

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
First, we identify $A$ and $B .$

Because $A = 0.5$ and $B = \frac{π}{2},$ we can find the stretching/compressing factor and period. The period is $\frac{π}{\frac{π}{2}} = 2,$ so the asymptotes are at $x = \pm 1.$ At a quarter period from the origin, we have

$\begin{array}{l} f (0.5) = 0.5 \tan (\frac{0.5 π}{2}) \\ = 0.5 \tan (\frac{π}{4}) \\ = 0.5 \end{array}$
This means the curve must pass through the points $(0.5, 0.5),$ $(0, 0),$ and $(- 0.5, −0.5) .$ The only inflection point is at the origin. Figure 2 shows the graph of one period of the function.

Figure 2

Your turn

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

Sketch a graph of $f (x) = 3 \tan (\frac{π}{6} x) .$

How did it go?

PreviousDetermining a Rider’s Height on a Ferris Wheel Next Graphing One Period of a Shifted Tangent Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 8.2, 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.