Answer:
[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Given : The measure of angle θ is 600°.
To find : The point (x, y) corresponding to θ on the unit circle is ?
Solution :
We know, In the unit circle, the x and y coordinates are the cosine and sine ratios, respectively.
Now, We have given θ = 600°
1 circle= 360°
So, 600° corresponds to 600° - 360° = 240°.
i.e, θ = 360° + 240°
180° < 240° < 270° ⇒ the point is in the third quadrant i.e, x and y coordinates are negative.
Now, The supplementary angle to use notable angles:
240° - 180° = 60°
The sine and cosine of 60° are known:
[tex]\sin 60^\circ = \frac{\sqrt{3}}{2}\\\\\cos 60^\circ= \frac{1}{2}[/tex]
In the unit circle the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.
Therefore, The coordinates are.
[tex]x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}[/tex]
