![]() ![]() They take on the value of 0 as well as positive and negative values of three numbers √3/2, √2/2, and ½. If we take a close look at the unit circle, we will find that the sin and cos values of angles fluctuate between -1 and 1. Finally, in quadrant IV, ‘Class’ only cosine is positive. In quadrant III, ‘Trig’ only tangent is positive. In quadrant II, ‘Smart’, only sine is positive. In quadrant I, which is ‘A’ all of the trigonometric functions are positive. To help remember which of the trigonometric functions are positive in each quadrant, we can use the mnemonic phrase ‘ All Students Take Calculus’ or All Sin Tan, Cos (ASTC).Įach of the four words in the phrase corresponds to one of the four quadrants, starting with quadrant I and rotating in counterclock-wise manner. 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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