Math Example--Angle Concepts--Using Trig Ratios to Measure Radians--Example 14

Topic

Angles

Description

This image shows a unit circle with a point at (-0.707, -0.707) in the third quadrant, and the highlighted arc is shown in red. The tangent ratio is calculated using these coordinates to find the angle in both radians and degrees.

Example 14: The tangent ratio is tan(Θ) = -0.707 / -0.707 = 1, leading to an inverse tangent of tan^-1(1) = 0.785 radians. Converting this to degrees gives Θ = 45° or -135°.

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.