Imagine a right triangle placed in a unit circle in the cartesian coordinate system. Applying Pythagoras’s theorem in a unit circle will help us understand trigonometric functions. Using a unit circle, we can calculate the trigonometric functions sine, cosine, and tangent. Finding Trigonometric Functions Using a Unit Circle The above equation satisfies all the points lying on the circle across the four quadrants. Here for the unit circle, the center lies at \((0,0)\) and the radius is \(1\ unit\). Equation of a Unit CircleĮquation of a Unit Circle: \(x^2 y^2 = 1\) This is simplified to obtain the equation of a unit circle. Hence the equation of the unit circle is \((x – 0)^2 (y – 0)^2 = 1^2\). A unit circle is formed with its center at the point \((0, 0)\), which is the origin of the coordinate axes. This equation of a circle is simplified to represent the equation of a unit circle. The general equation of a circle is \((x – a)^2 (y – b)^2 = r^2\), which represents a circle having the center \((a, b)\) and the radius \(r\). The locus of a point which is at a distance of one unit from a fixed point is called a unit circle. In trigonometry, the unit circle is useful for finding the trigonometric ratios sine, cosine, and tangent. The unit circle can be represented algebraically using the second-degree equation with two variables, x, and y. A unit circle is generally represented in cartesian coordinates. One unit circle is a circle with a radius of one unit. Here we shall learn the equation of the unit circle, and understand how to represent each of the points on the circumference of the unit circle, with the help of trigonometric ratios of \(\cos \theta\) and \(\sin \theta\). In addition, a unit circle is useful for calculating the standard angles of all trigonometric ratios. In addition to having all the properties of a circle, the unit circle is also derived from the equation of a circle. A circle is a closed geometric figure that has no sides or angles. A unit circle is a circle with a unit radius from its name alone.
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