The acute angle formed by the terminal side of an angle of 240 degrees and the x-axis is the subject of examination. In the context of trigonometry, this acute angle facilitates calculations involving trigonometric functions. For an angle of 240 degrees, situated in the third quadrant, determining this acute angle involves subtracting 180 degrees from the given angle. Therefore, 240 degrees minus 180 degrees yields 60 degrees. This resulting 60-degree angle represents the acute angle in question.
Identifying this acute angle is crucial because it provides a direct link to the trigonometric values of the original angle. The trigonometric functions (sine, cosine, tangent, etc.) of the initial angle, even when outside the range of 0 to 90 degrees, can be readily derived using the trigonometric values of this related acute angle and considering the quadrant in which the original angle lies. This process simplifies the evaluation of these functions and is a fundamental technique in trigonometry and related fields such as physics and engineering. Historically, this approach streamlined navigational calculations and various forms of mathematical modeling.
