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Exercises Trigonometry

Example 5 from Algebra and Trigonometry, 7.3 Unit Circle

Finding a Reference Angle

Find the reference angle of $225°$ as shown in Figure 18.

Graph of circle with 225-degree angle inscribed.

Figure 18

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
Because $225°$ is in the third quadrant, the reference angle is
$| (180° - 225°) | = | - 45° | = 45°$

Your turn

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

Find the reference angle of $\frac{5 π}{3} .$

How did it go?

PreviousUsing a Graphing Calculator to Find Sine and Cosine Next Using Reference Angles to Find Sine and Cosine

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.3, 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.