Because of the way the cartesian plane is designed, points that have a y-coordinate of 0 lie on the x-axis. Note that because the x-axis and y-axis are orthogonal to each other (i.e., they are in two different directions, at 90 degrees to each other) you could move 5 steps to the right and then 2 steps up, or vice versa, i.e., 2 steps up and then 5 steps to the right. Similarly, the y-coordinate or the ordinate specifies the vertical distance of the point from the origin and the sign indicates whether we should move up or down from the origin. We need to move 5 steps to the right (because it is a positive integer) and move 2 steps up (because again it is positive) to find the point, as shown below: Thus, the x-coordinate or the abscissa specifies the horizontal distance of your point from the origin and by looking at the sign we can glean whether we need to move right or left from the origin. Let us try to locate the point (5,2) on the cartesian plane. The x-coordinate is alternatively referred to as the abscissa and the y-coordinate is referred to as simply the ordinate. Thus, the origin has x-coordinate zero and the y-coordinate as zero as well. These two values are referred to as the x-coordinate and the y-coordinate, respectively. All points are specified relative to the origin and have two values. Locating points The origin of the cartesian plane is denoted by (0,0). The above figure gives you a handy way to remember the signs of quadrants. Finally, points in Quadrant IV (bottom, right) have x-values positive but y-values negative. Points in Quadrant III (bottom, left) have both x- and y-values to be negative. Points in Quadrant II (top, left) have x-values negative and y-values positive. ![]() Points in Quadrant I (top right) have x-values positive and y-values positive. ![]() The four quadrants As the picture above shows the quadrants are named Quadrants I, II, III, and IV starting from the (top, right) quadrant and moving in the counter-clockwise direction. In the cartesian plane, the x-axis and y-axis are at right angles to each other and the point at which they intersect is called the origin. As the name suggests, a quadrant means “one fourth” and refers to a quarter of the cartesian plane defined by the x- and y-axes. The cosine is the abscissa, that is to say, the x-coordinate or the horizontal value in a pair of coordinates.We will learn about quadrants in math, specifically quadrants in two dimensional cartesian geometry. The sine is the ordinate, that is to say, the y-coordinate or the vertical value in a pair of coordinates. Starting from $(1,0)$, the value of $\sin $ will be negative at any angle of the negative PQ line. ![]() In the unit circle, the coordinate axes delimit four quadrants that are numbered in an anti-clockwise direction. The x-axis is called abscissa and the y-axis is called ordinate. The reason to draw the circle on the origin is to cut the circle into 4 different quadrants with the help of an axis. Hence, the unit circle has its center at (0, 0) and its radius is one. The reason we call it a unit circle is because its radius is equal to $1$. To show how these trigonometric ratios are inter-related, imagine a unit circle. ![]() Trigonometry domain is so wide that it extends to the real numbers.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |