enter the coordinates of the point on the unit circle at the given angle. 150° (-√?/2, 1/ )
enter the coordinates of the point on the unit circle at the given angle. 150° (-√?/2, 1/ )
Answer
Explanation:
Step1: Find the reference angle
The reference angle of (150^{\circ}) is (180^{\circ}-150^{\circ} = 30^{\circ}).
Step2: Determine the coordinates using trigonometric functions
For a point ((x,y)) on the unit circle, (x=\cos\theta) and (y = \sin\theta). Since (150^{\circ}) is in the second quadrant ((x<0,y>0)), (\cos150^{\circ}=-\cos30^{\circ}=-\frac{\sqrt{3}}{2}) and (\sin150^{\circ}=\sin30^{\circ}=\frac{1}{2}).
Answer:
The number under the square - root is (3), and the value in the box for (y) - coordinate is (2). So the coordinates are (\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right))