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Chapter 4: Problem 108

What is a reference angle? Give an example with your description.

Short Answer

Expert verified
A reference angle is the acute angle formed by the terminal side of a given angle and the x-axis. As an example: if an angle is 130掳 (located in the second quadrant), its reference angle would be 50掳.

Step by step solution

01

Definition of Reference Angle

A reference angle is defined as the acute angle (angle with measure between 0 and 90 degrees) formed by the terminal side of a given angle and the x-axis. It's beneficial because it allows to find the trigonometric values of any angle. The values remain the same for each reference angle regardless in which quadrant it is located.
02

How to Calculate Reference Angle?

Depending on the quadrant, the reference angle (\(\theta'\)) is calculated differently: \n- In Quadrant I: \(\theta' = \theta\) \n- In Quadrant II: \(\theta' = 180掳 - \theta\) \n- In Quadrant III: \(\theta' = \theta - 180掳\) \n- In Quadrant IV: \(\theta' = 360掳 - \theta\) \nWhere \(\theta\) is the given angle.
03

Example of a Reference Angle

Let's take \(\theta = 130掳\) as an example. Here, \(\theta\) is located in the second quadrant. So, the reference angle \(\theta'\) will be: \n\(\theta' = 180掳 - 130掳 = 50掳\). Therefore, the reference angle for \(\theta = 130掳\) is 50掳.

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