Question

What are the coordinates of C

Answer 1

From the given figure

The radius of the circle is OC

Its length = the x-coordinate of point (1, 0), then

OC = 1

Let the x-coordinate of point C is x and the y-coordinate of it is y

We will use the trigonometry ratios to find x and y

Since the angle opposite to y and adjacent to x is 30 degrees, then

`\begin{gathered} \cos 30=(x)/(OC)=(x)/(1) \\ \cos 30=x \end{gathered}`

Since cos 30 = root3/2

`x=\frac{\sqrt[]{3}}{2}`
`\begin{gathered} \sin 30=(y)/(OC)=(y)/(1)=y \\ \cos 30=(1)/(2) \end{gathered}`

Then

`y=(1)/(2)`

The coordinates of point C are

`(\frac{\sqrt[]{3}}{2},(1)/(2))`