Question

Find the coordinate of the point (x,y) shown on the unit circle

Answer 1

Here the angle is

$\frac{4 \pi}{3}$

And radius is 1 units .

And

$x = r cos  \theta, y = r sin  \theta$

Substituting the values of theta and r, we will get

$x = 1 cos(\frac{4 \pi}{3} ) = -1/2 \\ y=1 sin( \frac{4 \pi}{3} ) =\sqrt3 /2$

So we will get

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

Answer 2

The coordinate of the point (x,y) shown on the unit circle is therefore: (-1/2, -√3/2)

The circle given is a unit circle.

In essence, the radius as indicated by the blue line is 1.

The angle subtended by the line is; 4π/3.

Therefore, from trigonometry of right-angled triangles; we have;

• x = r Cos(4π/3)

• y = r Sin(4π/3)

where, r = 1

Therefore,

• x = -1/2
• y = -√3/2

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