Question

How do you Identify the point (x,y) on the unit circle that corresponds to t=-3.14/2?

Answer 1

(x,y) coordinates of `t=-π/2` is `(0,-1)`

Explanation:

The unit circle is used for both degree measure and radian measure. In this case, `t=-π/2` is a radian measure.

Before we get to defining points on the unit circle in terms of radian measure, let's review the (x, y) coordinates of `sin` and `cos`.

At 0º, we know that `cos` is `1` and `sin` is `0` `(1,0)`

At 90º, `cos` is `0` and `sin` is `1` `(0,1)`

At 180º, `cos` is `-1` and `sin` is `0` `(-1,0)`

At 270º, `cos` is `0` and `sin` is `-1` `(0,-1)`

Now that we've reviewed those, we can start defining points on the unit circle. The difference between radians and degrees is that radians deal with the DISTANCE around the circle, while degrees deal with the MEASURE of the circle as it continues on.

We know that the circumference a circle is:

`C=2πr`

Since the unit circle has a radius of only one, a full revolution is `2π`.

Now all we have to do is use that to find `t=-π/2`.

We know that we if we divide `2π` by `-4`, we get our `-π/2.`

Also, we know that there are `360º` in a circle. Since we divided the `2π` by `-4`, we also divide `360º` by `-4`, since `2π` and `360º` are corresponding values.

When we solve that we get:

`t=-90º`

`-90º` is equal to `270º` and knowing that, we know that the (x,y) coordinate of `t=-π/2` is `(0,-1)`.