Answer:
[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
We are given that the measure of angle θ is 600° and we are to fin the point (x, y) corresponding to angle θ on the unit circle,
We know that the x,y coordinates in the unit circle are the cosine and sine ratios, respectively.
θ = 600
1 unit circle= 360°
It means that 600° corresponds to 600° - 360° = 240°.
So, θ = 360° + 240°
180° < 240° < 270° (this tells that the point is in the third quadrant and its coordinates are negative)
240° - 180° = 60° (using the supplementary angles to find the sin and cos)[tex]\sin 60^\circ = \frac{\sqrt{3}}{2}\\\\\cos 60^\circ= \frac{1}{2}[/tex]
Therefore, the x-coordinate is the cos of the given angle while y-coordinate is the sine of the given angle and the coordinates are:
[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]
