Using the fact that the radius of the unit circle is 1 (and therefore the hypotenuse of the right triangle is equal to 1), we can use the right triangle definitions of the trigonometric functions to find that, and. Together with θ, the angle formed between the initial side of an angle along the positive x-axis and the terminal side of the angle formed by rotating the ray counter-clockwise, we can form a right triangle. In the figure above, point A has coordinates of (x, y). Below is a figure showing all of the trigonometric relationships as they relate to the unit circle. The unit circle is often used in the definition of trigonometric functions. Unit circle definitions of trigonometric functions This is true for all points on the unit circle, not just those in the first quadrant, and is useful for defining the trigonometric functions in terms of the unit circle. Based on the Pythagorean Theorem, the equation of the unit circle is therefore: The hypotenuse of the right triangle is equal to the radius of the unit circle, so it will always be 1. When a ray is drawn from the origin of the unit circle, it will intersect the unit circle at a point (x, y) and form a right triangle with the x-axis, as shown above. It is commonly used in the context of trigonometry. Home / trigonometry / unit circle Unit CircleĪ unit circle is a circle with radius 1 centered at the origin of the rectangular coordinate system.
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