What do the coordinates of a point on the unit circle represent?
Like all functions, the sine function has an input and an output. Its input is the measure of the angle; its output is the y-coordinate of the corresponding point on the unit circle. The cosine function of an angle t equals the x-value of the endpoint on the unit circle of an arc of length t.
What are the coordinates of the point on the unit circle at the given angle?
Just remember that coordinates on the unit circle can be derived using: (x, y) = (cos A, sin A), where A is the measurement of the angle. In this case, A=4π3 .
How do you find the coordinates of a terminal point?
To find the terminal point on the unit circle, start at (1,0), measure the angle in degree or radian on the circle (move counter clockwise if the angle is positive and clockwise if the angle is negative.) The coordinate of the endpoint is called the terminal point.
What are the coordinates of 60 on the unit circle?
#1: Memorize Common Angles and Coordinates
| Angle (Degrees) | Angle (Radians) | Coordinates of Point on Circle |
|---|---|---|
| 0° / 360° | 0 / 2π | (1, 0) |
| 30° | π 6 | ( √ 3 2 , 1 2 ) |
| 45° | π 4 | ( √ 2 2 , √ 2 2 ) |
| 60° | π 3 | ( 1 2 , √ 3 2 ) |
How do you find a missing coordinate on a unit circle?
How to Find a Missing Coordinate on a Unit Circle
- Substitute the x-coordinate value into the unit-circle equation.
- Square the x-coordinate and subtract that value from each side.
- Take the square root of each side.
What are the coordinates of 180 on the unit circle?
#1: Memorize Common Angles and Coordinates
| Angle (Degrees) | Angle (Radians) | Coordinates of Point on Circle |
|---|---|---|
| 135° | 3 π 4 | ( − √ 2 2 , √ 2 2 ) |
| 150° | 5 π 6 | ( − √ 3 2 , 1 2 ) |
| 180° | π | (-1, 0) |
| 210° | 7 6 | ( − √ 3 2 , − 1 2 ) |
What are the coordinates of the point on the unit circle that corresponds to 180?
How do you know if a coordinate is on the unit circle?
Explanation: The unit circle is by definition a circle with radius equal to 1 and center (0,0), so the distance of the points (x,y) in that circle to the center is equal to 1, hence by the distance formula : √a2+b2=1⟺a2+b2=1. If it equals 1, it is on the unit circle.