Question

The measure of angle θ is 600°. The point (x, y) corresponding to θ on the unit circle is ______.

Answer 1

A unit circle has a radius of 1. 

Θ = 600°

1 circle = 360°

Θ = 360° + 240°

(x,y) =  cos 360° , sin 240° 
(x,y) = -0.50 , -0.886

If these were the given choices: 
A.) -(3^(1/2))/2     B.)-1(2^(1/2))/2           C.)-1/2         D.) (3^(1/2))/2

x = C) - 1/2
y = A) -(3^1/2) / 2

Answer 2

Answer:

$x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}$

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:

$\sin 60^\circ = \frac{\sqrt{3}}{2}\\\\\cos 60^\circ= \frac{1}{2}$

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.

$x= -\frac{1}{2}\\\\ y= -\frac{\sqrt{3}}{2}$