Precalculus: Triangle Trigonometry and Circles

Objectives

• Students will understand that trigonometric functions of an angle do not depend on the size of the triangle within which the angle is contained, but rather on the ratios of the sides of the triangle.
• Students will understand the meaning of reference angles and use reference angles to determine the trigonometric functions of a given angle.
• Students will create an algorithm to determine the trigonometric functions of an angle based on its reference angle.

Vocabulary

• hypotenuse
• horizontal and vertical legs
• trigonometric functions
• reference angle

About the Lesson

This lesson involves the ratios of side lengths of triangles with invariant angle measures and the relationships to trigonometric functions of an angle.

As a result, students will:

• Manipulate the radius of a circle to change the dimensions of a triangle with fixed angles and observe the resulting ratios of side lengths.
• Make and test predictions about the impact of side lengths and the quadrant in which the reference triangle is located on the trigonometric functions of an angle.