For example, suppose we know that the x-coordinate of a point on the unit circle is \(-\dfrac{1}{3}\). origin and that is of length a. In this section, we studied the following important concepts and ideas: This page titled 1.1: The Unit Circle is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Ted Sundstrom & Steven Schlicker (ScholarWorks @Grand Valley State University) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. If you pick a point on the circle then the slope will be its y coordinate over its x coordinate, i.e. This line is at right angles to the hypotenuse at the unit circle and touches the unit circle only at that point (the tangent point). Did the Golden Gate Bridge 'flatten' under the weight of 300,000 people in 1987? Find the Value Using the Unit Circle -pi/3. So this theta is part So essentially, for Unit Circle: Quadrants A unit circle is divided into 4 regions, known as quadrants. And what is its graph? The interval (\2,\2) is the right half of the unit circle. This page exists to match what is taught in schools. Now that we have The unit circle is is a circle with a radius of one and is broken down using two special right triangles. angle, the terminal side, we're going to move in a of what I'm doing here is I'm going to see how But whats with the cosine? Find two different numbers, one positive and one negative, from the number line that get wrapped to the point \((0, -1)\) on the unit circle. Well, we just have to look at 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. This equation of a circle is simplified to represent the equation of a unit circle. So the sine of 120 degrees is the opposite of the sine of 120 degrees, and the cosine of 120 degrees is the same as the cosine of 120 degrees. intersects the unit circle? The point on the unit circle that corresponds to \(t =\dfrac{2\pi}{3}\). Then determine the reference arc for that arc and draw the reference arc in the first quadrant. You read the interval from left to right, meaning that this interval starts at $-\dfrac{\pi}{2}$ on the negative $y$-axis, and ends at $\dfrac{\pi}{2}$ on the positive $y$-axis (moving counterclockwise). When memorized, it is extremely useful for evaluating expressions like cos(135 ) or sin( 5 3). What does the power set mean in the construction of Von Neumann universe. over the hypotenuse. ","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["academics-the-arts","math","calculus"],"title":"How to Measure Angles with Radians","slug":"how-to-measure-angles-with-radians","articleId":190935},{"objectType":"article","id":187457,"data":{"title":"Assign Negative and Positive Trig Function Values by Quadrant","slug":"assign-negative-and-positive-trig-function-values-by-quadrant","update_time":"2016-03-26T20:23:31+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Trigonometry","slug":"trigonometry","categoryId":33729}],"description":"The first step to finding the trig function value of one of the angles thats a multiple of 30 or 45 degrees is to find the reference angle in the unit circle. So an interesting \[x^{2} + (\dfrac{1}{2})^{2} = 1\] Some negative numbers that are wrapped to the point \((0, -1)\) are \(-\dfrac{3\pi}{2}, -\dfrac{5\pi}{2}, -\dfrac{11\pi}{2}\). Connect and share knowledge within a single location that is structured and easy to search.