In the same way, we can calculate the values of the other trigonometric ratios by using the right-angled triangle within the unit circle. We now have sinθ = y, cosθ = x, and using this we now have tanθ = y/x. We can find the values of the trigonometric ratio by applying this in trigonometry: We now have a right angle triangle that has sides 1, x, and y. Right triangles have a base and an altitude, which are represented by the values of x and y. The radius vector forms an angle θ with the positive x-axis and the coordinates of the endpoint of the radius vector is (x, y). The circumference of the circle is the hypotenuse of the triangle. Consider a right triangle placed within a unit circle in the cartesian coordinate plane. In order to understand trigonometric functions, let us apply the Pythagoras theorem to a unit circle. The trigonometric functions sine, cosine, and tangent can be calculated using a unit circle. Finding Trigonometric Functions Using a Unit Circle All the points in the circle and in the quadrants, according to the above equation, are satisfied. The center of the unit circle lies at (0,0) and the radius is 1 unit. A simplified version of this equation is shown below. Hence the equation of the unit circle is (x – 0) 2 + (y – 0) 2 = 1 2. A unit circle is made with its center at the point(0, 0), which is the origin of the coordinate axes. This equation can be 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 describes a circle having the center (a, b) and the radius r. Unit Circle DefinitionĪs the locus of a point that is one unit away from a fixed point, it is commonly referred to as a unit circle. In trigonometry, the unit circle is useful in finding the values of the trigonometric ratios sine, cosine, and tangent. The unit circle is algebraically represented by the second-degree equation with two variables x and y. A unit circle is generally represented in the cartesian coordinate system. Unit Circle and Trigonometric IdentitiesĬircles with radii of one unit are called unit circles.Finding Trigonometric Functions Using a Unit Circle.
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