This can be answered by understanding the unit circle and the Pythagorean theorem. 210° can form a right triangle with the x-axis in quadrant III. To get the value of the angle formed between the circle’s radius and the x-axis, divide the angles of the 2 quadrants from 210°.
210°-90-°90° = 30°
In the Pythagorean theorem has a ratio of 1,2, √3 of the sides of the triangle. In a unit circle, the opposite side from the 30° angle is 1. The adjacent side is √3 while the hypotenuse is 2. With this info, we can use SOHCAHTOA.
So,
Sin(∅) = opposite / hypotenuse
Sin(30°) = ½ =0.5
Cos(∅) = adjacent/hypotenuse
Cos(30°) = sqrt.3/2 = 0.86602 = 0.87
