Abstract

Determining exact values of trigonometric ratios remains an integral part of the high school mathematics curriculum. Students learn to use 45-45-90° triangles and 30-60-90° triangles to determine exact function values of angles of 30°, 45°, and 60°. Such exact-value ratios can help to determine trigonometric ratios for nonstandard angle measures when trigonometric identities and algebra are used. In this lesson, students apply a geometric approach to determine exact-value trig ratios for angle measures of 22.5°, 67.5°, 15°, and 75°. Some students can extend that approach to other nonstandard angle measures.

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