The only difference in what you type, and the way Graphmatica detects a polar graph, is that you must use the variables t and r instead of x and y. Polar graphs can be typed in the equation combobox just like normal graphs. The domain for the graphing is 0 to 2pi (the first complete circle in the positive direction), but you can easily change these values using the Theta Range function in the Options menu. To make a graph using polar coordinates, we let theta be the independent variable and calculate a distance to plot out from the origin as we let the angle sweep around in the positive direction. To put a polar coordinate into Cartesian terms in order to graph it, we use the equations: x = r cos t and y = r sin t. There are 2pi radians in a complete circle, corresponding to 360 of the degrees you're familiar with. The direction is measured in radians as an angle starting from the positive side of the x-axis and turning around counter-clockwise (like measuring the angle the hand on a clock has traveled starting at the 3 o'clock position and going backwards). The t tells what direction to go in from the origin, and the r tells how far to go out in that direction to reach the point. The traditional Cartesian method relies on an x and a y coordinate to mark how far a point is from the axes in two perpendicular directions polar coordinates plot the location of a point by one coordinate represented by the Greek letter theta which is simplified to t in Graphmatica and another called r. The concept is pretty easy to grasp graphically, but if you have never used polar coordinates and want to understand them, you should probably read the section below. The angle to the positive x-axis (rotating in the typical counter-clockwise fashion) is 120°.Polar coordinates are a fundamentally different approach to representing curves in two-dimensional space. Remember, this is the reference angle not the angle to the positive x-axis. Since we already know the angle exists in the second quadrant, only positive values are being used. Now, we must calculate the angle using the second conversion equation (if you do not recognize the special right triangle). Assuming you do not recognize the triangle, let us view the calculation using the first conversion equation. It is unnecessary to calculate the length of the hypotenuse if you recognize this special right triangle. Here is a diagram of the point in the second quadrant. So, the final answer, written as (r, θ), is…Įxample 2: Convert (-1, √3) from rectangular form to polar form. Since the angle exists in the fourth quadrant, we have to account for the traditional trigonometric angle relative to the positive x-axis with a counter-clockwise motion. Remember, this angle is the reference angle. To get the distance the point is from the origin, which is the r-value, we will use the first conversion equation, like so. Here is the graph of the rectangular point. It is helpful to get a diagram to see what is going on. Now, let us look at two examples to see how these conversions are done.Įxample 1: Convert (5,-3) to polar form, rounded to the nearest tenth. Using knowledge of trigonometry, we can see the tangent of theta is equal to the opposite (y) over adjacent (x) sides, which is the second conversion equation. Since this is a right triangle, we can employ The Pythagorean Theorem, which is the first of the two conversion equations. The relationship between the x, y, and r-variables should be familiar. To understand the genesis of these equations, examine this diagram. To convert from rectangular to polar coordinates requires different equations.
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