Trigonometric Functions of Acute Angles

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Presentation transcript:

Trigonometric Functions of Acute Angles 4.2 Trigonometric Functions of Acute Angles

What you’ll learn about Right Triangle Trigonometry Two Famous Triangles Evaluating Trigonometric Functions with a Calculator Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name.

Standard Position An acute angle θ in standard position, with one ray along the positive x-axis and the other extending into the first quadrant.

Trigonometric Functions

Example Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º.

Example Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º.

Example Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º.

Example Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º.

Common Calculator Errors When Evaluating Trig Functions Using the calculator in the wrong angle mode (degree/radians) Using the inverse trig keys to evaluate cot, sec, and csc Using function shorthand that the calculator does not recognize Not closing parentheses

Example Solving a Right Triangle

Example Solving a Right Triangle

Quick Review 1. Solve for x. x 3 2 2. Solve for x. 6 3 x

Quick Review

Quick Review Solutions 1. Solve for x. x 3 2 2. Solve for x. 6 3 x

Quick Review Solutions