Math Example--Angle Concepts--Using Trig Ratios to Measure Radians--Example 6

Topic

Angles

Description

This image shows a unit circle with a highlighted arc in the second quadrant. The point (-0.707, 0.707) is marked on the circle. The caption explains how to find the radian measure of the highlighted arc using trigonometric ratios. The arc is in red, and the radius is drawn.

Example 6: The tangent ratio is calculated using tan(Θ) = 0.707 / -0.707 = -1. The inverse tangent is found as tan^-1(-1) = -0.785 radians, and converting this to degrees gives Θ = -45 degrees or 135 degrees.

These examples cover trigonometric ratios by demonstrating specific angles and calculations on the unit circle. Such visualizations aid in understanding the fundamental concepts of trigonometric functions.

By studying multiple worked-out examples, students gain deeper insight into the concept and can better recognize patterns in trigonometric functions.

Teacher's Script: Let's look at this example together. Notice how the angle is highlighted and how the tangent ratio is calculated. This visual can help you understand how trigonometric ratios work on a unit circle.

For a complete collection of math examples related to Trig Ratios click on this link: Math Examples: Trig Ratios and Radian Measures Collection.