Algebra and Trigonometry, 5th Edition

6.1 Trigonometric Functions of Acute Angles

• Determine the six trigonometric ratios for a given acute angle of a right triangle.

• Determine the trigonometric function values of $30°$ , $45°$ , and $60°$ .

• Using a calculator, find function values for any acute angle, and given a function value of an acute angle, find the angle.

• Given the function values of an acute angle, find the function values of its complement.

The Trigonometric Ratios

We begin our study of trigonometry by considering right triangles and acute angles measured in degrees. An acute angle is an angle with measure greater than $0°$ and less than $90°$ . Greek letters such as $\alpha$ (alpha), $\beta$ (beta), $\gamma$ (gamma), $\theta$ (theta), and $\varphi$ (phi) are often used to denote an angle. Consider ...