Math Example--Angle Concepts--Using Trig Ratios to Measure Radians--Example 15

Topic

Angles

Description

This image shows a unit circle with a point at (-0.866, -0.5), and the highlighted arc in red appears in the third quadrant of the circle. The tangent ratio is calculated using these coordinates, followed by finding the angle in both radians and degrees.

Example 15: The tangent ratio is tan(Θ) = -0.5 / -0.866 = 0.577, leading to an inverse tangent of tan^-1(0.577) = 0.524 radians. Converting this to degrees gives Θ = 30° or -150°.

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.