Math Example--Angle Concepts--Using Trig Ratios to Measure Radians--Example 3

Topic

Angles

Description

The image shows a unit circle with a highlighted arc and a point labeled (0.5, 0.866) on the circumference, connected by a tangent line from the origin to this point. The solution process for finding the angle measure is shown on the right side.

Example 3: The tangent ratio is calculated as tan(Θ) = 0.866 / 0.5 = 1.732. The inverse tangent is found as tan^-1(1.732) = 1.047 radians. This is converted to degrees: Θ = 1.047 * (180 /π) = 60°.

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.