Unit 7: Right Triangles & Trigonometry Homework 6: Trigonometry Review

This page covers a variety of trigonometry problems, focusing on simplifying trigonometric ratios and solving for unknown angles and sides in right triangles. The exercises are designed to reinforce understanding of trigonometric ratios and their applications.

Highlight: This is a two-page document, emphasizing the comprehensive nature of the review.

The first section requires students to express trigonometric ratios as fractions in their simplest form. For example:

Example: In a right triangle with hypotenuse 29 and one side 20, students are asked to find sin D, cos D, and tan D.

Solutions:

• sin D = 20/29
• cos D = 21/29
• tan D = 20/21

The second section involves solving for unknown angles or sides in right triangles using trigonometric functions. Students are instructed to round their answers to the nearest tenth when applicable.

Vocabulary: Inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) are used to find unknown angles.

Examples of problems in this section include:

1. Finding an angle using cos⁻¹(14/15), resulting in 21°.
2. Calculating a side length using sin 48° = x/32, yielding x ≈ 23.8.
3. Determining an angle using tan⁻¹(19/23), resulting in 39.6°.

Definition: Trigonometric ratios are relationships between the sides of a right triangle and its angles, fundamental to solving problems in trigonometry.

The worksheet provides a comprehensive review of trigonometric ratios, their simplification, and application in solving right triangle problems, serving as an excellent Unit 8 Right Triangles and Trigonometry Homework resource.