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Understanding Special Right Triangles and Trigonometric Functions

This section delves into right triangle trigonometry, specifically focusing on special right triangles such as the 30-60-90 and 45-45-90 triangles. It introduces the unit circle, defining key elements like the hypotenuse and radius. The section also explains the acronym SOHCAHTOA, which helps memorize the definitions of sine, cosine, and tangent. By understanding these fundamental concepts and identities, students will learn to evaluate trigonometric functions and apply them in various mathematical scenarios. Worksheets are provided for practice.

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Understanding Special Right Triangles and Trigonometric Functions

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  1. Trigonometry Section 4.3 Right Triangle Trigonometry

  2. Special Right Triangles • A unit circle has a radius of _____. • The hypotenuse is _____ of a triangle. • The hypotenuse of the triangles inside the unit circle has a length of _____. • Special triangle 30-60-90 • Special triangle 45-45-90 • Fill in the unit circle.

  3. SOHCAHTOA • SOHCAHTOA is an acronym to help us remember the right triangle definitions. • S stands for _____. • C stands for _____. • T stands for _____. • O stands for _____. • A stands for _____. • H stands for _____.

  4. Right Triangle Definitions of Trig Functions • Therefore, SOH means _____. • CAH means _____. • TOA means _____. • Adjacent and opposite are terms relative to the _____. • Sine, cosine, and tangent are ratios of triangles. • So why are sine and cosine always between -1 and 1?

  5. Evaluating Trig Functions • Ex 1 • Memorize all identities • Reciprocal identities • Quotient identities • Pythagorean identities • Ex 4 • Ex 5 • Ex 7

  6. Homework • Worksheets 3 & 4 • 1-60, Applications 61-66

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