Unit circle chart how to#

The following table shows degree to radian conversions for the angles in the unit circle. Try these tricks to memorize the unit circle without needing to remember every coordinate. There are a few tricks you can use to memorize the unit circle. The unit circle might intimidate you, but remembering it might be easier than it might seem at first glance. Unit Circle Chart Table showing the angles and coordinates in the unit circle chart. Therefore, when using the unit circle with an angle greater than 360 degrees/2π radians, you should subtract 360 degrees/2π radians repeatedly until the angle is between 0 and 360 degrees/2π radians. Note that the unit circle repeats after 360 degrees or 2π radians. The chart shows the angles in radians and degrees, and shows each coordinate solved using the special right triangle created using the unit circle. The unit circle chart shows the angles used in the 30-60-90 and 45-45-90 special right triangles, and the coordinates where the radius intersects the edge of the unit circle. (cos θ, sin θ) Unit Circle Chart with Radians and Degrees Thus, the coordinate where the radius intersects the circle is: The length of the base of the triangle is equal to the cosine of the angle, which becomes the x-coordinate.

Unit circle chart how to#

How to Find Coordinates on the Unit Circleįor a specified angle, the point, or coordinate, where the radius intersects the circle can be calculated using trigonometric functions.Īs noted above, the height of the right triangle formed is equal to the sine of the angle θ this becomes the y-coordinate. Since the radius of the unit circle is 1, the length of the right triangle’s hypotenuse is equal to 1.Īs seen in the image above, the height of the triangle (leg a) is equal to the sine of the angle, while the length of the base of the triangle (leg b) is equal to the cosine. The unit circle defines how to find the length of the sides of a right triangle formed when extending a line from the origin to the edge of the circle for a known angle.