# Lesson 5:

Trigonometric Ratios

## Clarifying the Learning

### Lesson Overview

In this lesson you will discover the trigonometric ratios, use them to solve for missing measures in right triangles, and prove the Pythagorean Identity (sin2x+cos2x=1). What is trigonometry? Trigonometry means “the study of triangles.” Triangles are so important that In a traditional math sequence, there is an entire course dedicated to trigonometry. In Math II, we will learn the basics of trigonometry; in Math III and Math IV, you will study trigonometry in more detail. In this lesson, we are going to look at how trigonometric ratios can help us to solve problems that have missing angle or side measures in right triangles.

### Driving Question

What is trigonometry and how can I use it to solve problems involving right triangles?

## Defining Success

### Content Standards and Objectives:

After completing this lesson, you should understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.**(M.2HS.STP.10)(CCSS.Math.Content.HSG-SRT.C.6)**

Upon mastering this objective, you should be able to conduct the tasks in the video below:

You should also be able to Explain and use the relationship between the sine and cosine of complementary angles.**(M.2HS.STP.11)(CCSS.Math.Content.HSG-SRT.C.7)**

Upon mastering this objective, you should be able to conduct the tasks in the video below:

After completing this lesson, you should be able to use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.**(M.2HS.STP.12)(CCSS.Math.Content.HSG-SRT.C.8)**

Upon mastering this objective, you should be able to conduct the tasks in the video below:

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