Question

What are the coordinates of the terminal determined by t = 20 3

Answer 1

As per given by the question,

There are given that the terminal point,

`t=(20\pi)/(3)`

Now,

To find the terminal point, there are use the refrence point,

`t=(2\pi)/(3)`

That means,

The given angle is equivalent to the angle ,

`t=(2\pi)/(3)`

Now,

According to the terminal point concept,

The radius of the unit circle at that point makes a right angle with the coordinates of the terminal point and,

There is also noted that the given terminal is on the 2nd quadrant of the cpordinate axis.

So,

The x value of the terminal point is negative and y value is positive.

Then,

There is use the relation,

`-\cos (\pi-(2\pi)/(3))=(x)/(1)`

Because the radius of the uit circle is 1.

Now,

`\begin{gathered} -\cos (\pi-(2\pi)/(3))=(x)/(1) \\ -\text{cos(}(\pi)/(3))=x \\ x=-(1)/(2) \end{gathered}`

Then,

Similarly to find the y-coordinate.

So,

Here, find the y-coordinate to relate the sine trigonometric function.

`\begin{gathered} \sin (\pi-(2\pi)/(3))=(y)/(1) \\ \sin ((\pi)/(3))=y \\ y=\frac{\sqrt[]{3}}{2} \end{gathered}`

The coordinate of the terminal point is,

`(x,\text{ y)=(-}(1)/(2),\text{ }\frac{\sqrt[]{3}}{2})`

Hence, the option A is correct.