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

Feb 23, 2018

(x,y) coordinates of t=-π/2 is $\left(0 , - 1\right)$

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 $0$ $\left(1 , 0\right)$

At 90º, $\cos$ is $0$ and $\sin$ is $1$ $\left(0 , 1\right)$

At 180º, $\cos$ is $- 1$ and $\sin$ is $0$ $\left(- 1 , 0\right)$

At 270º, $\cos$ is $0$ and $\sin$ is $- 1$ $\left(0 , - 1\right)$

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 $\left(0 , - 1\right)$.