Geometry

Question Analysis  

The task is to find the coordinates on the unit circle at 330° using the trigonometric ratios from special angles in Quadrant I (30 - 45 - 60). The key is to leverage the symmetry of the unit circle and the relationships between angles in different quadrants.

 

Key Concept Explanation  

Unit Circle Coordinates: For any angle θ, the coordinates of the corresponding point on the unit circle are (cos θ, sin θ).

Quadrantal Relationships: Angles in Quadrant IV (270° - 360°) share reference angles with those in Quadrant I. The reference angle for 330° is 30° (360° - 330°), and trig values in Quadrant IV follow the pattern of cos (+), sin (-) based on the ASTC rule.

 

Step-by-Step Solution  

1. Identify the reference angle:  

The reference angle for 330° is 30°.

2. Determine the cosine and sine values:  

In Quadrant I, for a 30° angle,  and .

In Quadrant IV, cosine is positive and sine is negative. So for 330°, , and

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