Find the reference angle for the given angle. (a) 150^∘ (b) 330^∘ (c) -30^∘

Name: Problem 3, Chapter 6: Algebra and Trigonometry
Uploaded: 2020-07-19T21:11:33-08:00
Duration: 3 min 5 s
Channel: Noraney Ocampo
Description: Find the reference angle for the given angle. (a) 150^∘ (b) 330^∘ (c) -30^∘

step 1 So you want to find the reference angles for 150 degrees, for 330, and for 330, and for negative

Find the reference angle for the given angle. (a) ...

Key Concepts

Reference Angle

A reference angle is the acute angle formed between the terminal side of an angle in standard position and the horizontal x-axis. It is always the smallest angle to the x-axis and is used to simplify the evaluation of trigonometric functions for angles in any quadrant.

Angles in Standard Position

An angle is said to be in standard position when its vertex is at the origin and its initial side lies along the positive x-axis. The terminal side indicates the angle's measure, and its position relative to the quadrants helps determine the calculation of its reference angle.

Quadrant Determination

To determine the reference angle, it is crucial to identify which quadrant the terminal side of the angle lies in. The rules differ by quadrant: for angles in the first quadrant, the reference angle is the angle itself; in the second quadrant, it is the difference between 180° and the angle; in the third quadrant, it is the angle minus 180°; and in the fourth quadrant, it is the difference between 360° and the angle.

Handling Negative Angles

For angles measured in the clockwise direction (negative angles), it is important to first find a co-terminal angle by adding 360° (or an appropriate multiple of 360°) until the angle becomes positive. Once the angle is expressed in standard position, the same techniques for finding reference angles in the appropriate quadrant can be applied.

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