More Lessons for Trigonometry
In this lesson we will look at Evaluating Trigonometric Functions Using the Reference Angle.
The following figures give examples of the standard angle and the reference angle for the different quadrants. Scroll down the page for more examples and solutions.
What is The Reference Angle Theorem?
The Reference Angle Theorem states that
To find the value of a trigonometric function of any angle t:
1. Determine the function value for the associated reference angle t'.
2. Depending on the quadrant in which t lies, the answer will be either be + or -.
How to evaluate trig functions using reference angles?
1. Find the reference angle for the given angle.
2. Rewrite the original trig function with the reference angle.
3. Affix the appropriate sign to the trig function (+ or -), depending which quadrant the angle terminates in.
4. Evaluate the trig function.
Evaluating Trigonometric Functions Using Reference Angles
Evaluating Trigonometric Functions Using the Reference Angle, Example 1
A quick review of the unit circle in quadrant 1 and discuss how to use the reference angle to evaluate some trig functions
Evaluating Trigonometric Functions Using the Reference Angle, Example 2
Discuss how to use the reference angle to evaluate some more trig functions.
Evaluating Trig functions using reference angles
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.