Choose the point on the terminal side of -210°.
well, for 30° it is (1/2, √3/2)
Now move that around 180°
To choose the point on the terminal side of an angle, we need to find the coordinates (x, y) of the point on the unit circle that corresponds to that angle.
First, let's find the reference angle, which is the positive acute angle between the terminal side of the angle and the x-axis.
To find the reference angle for -210°, we can use the fact that a full revolution is 360°. Since -210° is in the third quadrant (clockwise direction), we can calculate the reference angle by subtracting 180° from it:
Reference angle = -210° - (-180°)
= -210° + 180°
= -30°
Next, we need to find the coordinates (x, y) on the unit circle corresponding to the reference angle of -30°.
On the unit circle, the x-coordinate of a point is given by the cosine of the angle, and the y-coordinate is given by the sine of the angle.
Using a calculator, we can find the cosine and sine values for -30°:
cos(-30°) ≈ 0.866
sin(-30°) ≈ -0.5
Therefore, the coordinates (x, y) on the unit circle corresponding to -30° are approximately (0.866, -0.5).
So, the point on the terminal side of -210° is (0.866, -0.5).