![unit circle unit circle](https://i.ytimg.com/vi/BYuAR9KqcOE/maxresdefault.jpg)
It's just easier that way.) So you'll probably be expected to have memorized the trig-function values for these angles. (Strictly speaking, 0deg and 90deg aren't "in" any quadrant, but we'll work with them as though they were in the first quadrant. As students to consider a point P (x, y) on the unit circle with radius r 1, making an angle with x-axis. Now that students understand what a unit circle is, you can proceed by explaining trigonometric functions on it. These angles, in the first quadrant (being the "reference" angles) are 0°, 30°, 45°, 60°, and 90°. Trigonometric Functions on a Unit Circle. The circumfrence of the unit circle is 2.
![unit circle unit circle](https://img.wagnerrealty.com/Homes/Images/Listings/154924666/1/08cb49eae9b562c4d28b79d64702ba1c/Photo.jpg)
Also, since tangent involves dividing by x, and since x = 0 when you're one-fourth and three-fourths of the way around the circle (that is, when you're at 90° and at 270°), the tangent will not be defined for these angle measures.Ĭertain angles have "nice" trig values. The unit circle is the circle whose center is at the origin and whose radius is one. The radius of a unit circle can be taken at any point on the perimeter of the circle. The unit circle is actually referred to as a circle of radius one suspended in a specific quadrant of the coordinate system. Working from this, you can take the fact that the tangent is defined as being tan(θ) = y/ x, and then substitute for x and y to easily prove that the value of tan(θ) also must be equal to the ratio sin(θ)/ cos(θ).Īnother thing you can see from the unit circle is that the values of sine and cosine will never be more than 1 or less than −1, since x and y never take on values outside of this interval. The interactive unit circle is what that joins the trigonometric functions - sine cosine, and tangent, and the unit circle. For instance, in the unit circle, for any angle θ, the trig values for sine and cosine are clearly nothing more than sin(θ) = y and cos(θ) = x. The point of the unit circle is that it makes other parts of the mathematics easier and neater.