![]() The sign of a trigonometric function depends on the quadrant that the angle is found. Sin 2 θ + cos 2 θ = 1 Sign of Trigonometric Functions Since, the equation of a unit circle is given by x 2 + y 2 = 1, where x = cos θ and y = sin θ, we get an important relation: Applying this values in trigonometry, we getĬosec θ = 1/sin θ = Hypotenuse/ Altitude = 1/y Thus we have a right triangle with sides measuring 1, x, y. The lengths of the two legs (base and altitude) have values x and y respectively. The radius of the unit circle is the hypotenuse of the right triangle, which makes an angle θ with the positive x-axis. By drawing the radius and a perpendicular line from the point P to the x-axis we will get a right triangle placed in a unit circle in the Cartesian-coordinate plane. Being a unit circle, its radius ‘r’ is equal to 1 unit, which is the distance between point P and center of the circle. Let us take a point P on the circumference of the unit circle whose coordinates be (x, y). Here we will use the Pythagorean Theorem in a unit circle to understand the trigonometric functions. We can calculate the trigonometric functions of sine, cosine, and tangent using a unit circle. Finding the Angles of Trigonometric Functions Using a Unit Circle: Sin, Cos, Tan ![]() The above equation satisfies all the points lying on the circle in all four quadrants.
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