Geometry

Question Analysis  

The question aims to find the unit circle coordinates for 300° by leveraging the trigonometric ratios of 30 - 45 - 60 angles in Quadrant I, focusing on the relationship between angles in different quadrants and the sign changes of trig functions.

 

Key Concept Explanation  

For any angle θ on the unit circle, the coordinates of the corresponding point are given by (cos θ, sin θ).

Angles in Quadrant IV (270° - 360°) have reference angles related to those in Quadrant I. The reference angle for 300° is 60° (360° - 300°). According to the ASTC rule, cosine is positive and sine is negative in Quadrant IV.

 

Step-by-Step Solution  

1. Determine the reference angle:  

The reference angle for 300° is 60°.

2. Recall the trigonometric ratios from Quadrant I:  

For a 60° angle in Quadrant I, and .

3. Adjust the signs based on the quadrant:  

Since 300° is in Quadrant IV,   (cosine is positive in QIV), and