Short Answer 
The unit circle, centered at (0, 0) with a radius of 1, is essential for understanding trigonometric functions. The angle **6 5 œÄ** is in the second quadrant, where sine values are positive, and its reference angle leads to the conclusion that **sin (6 5 œÄ) = 1/2**, contradicting Joslah’s claim of **-2/3**.
Step 1: Understanding the Unit Circle
Begin by familiarizing yourself with the unit circle, which is a circle centered at the origin (0, 0) with a radius of 1. Angles on the unit circle are measured in radians, where a full circle corresponds to 2 π radians (or 360 degrees). Recognizing these fundamentals is essential for interpreting trigonometric functions.
Step 2: Locating the Angle on the Unit Circle
Next, determine where the angle 6 5 π lies on the unit circle. This angle is located in the second quadrant, and can be converted to degrees, yielding 150 degrees. In the second quadrant, the sine values are positive, which indicates that we can expect a positive sine result for this particular angle.
Step 3: Calculating the Sine Value
Finally, calculate the sine of 6 5 œÄ using the reference angle approach. The reference angle is found by calculating œÄ – 6 5 œÄ, giving you 6 œÄ. The sine of 6 œÄ (equivalent to 30 degrees) is 1/2. Therefore, Joslah’s claim that sin (6 5 œÄ) = -2/3 is incorrect; the accurate value of sin (6 5 œÄ) is indeed 1/2.