Graphing equations is a simple process that can be learned without requiring a math genius or straight-A student. It involves plotting points, using tables, and graphing utilities to visualize algebraic equations, add sliders, and animate graphs. Learn how to plot linear equations with one or two variables, including two-variable equations.
Plotting points involves filling in the table with the calculated y-values and plotting them on the coordinate plane. Each point represents an x-value from the domain with its corresponding y. The representation of a linear equation in the form of y=mx+b on a graph is called graphing linear equations.
Graphing linear equations can be parametric (x(t), y(t), z(t)), which has more freedom and can be a line or a plane. In this section, we examine the equations of lemniscate equations, finding the domain of θ, and using a graphing utility like Desmos to plot polar equations and find the area of the common interior region.
To graph in the polar coordinate system, construct a table of θ and r values, enter values of θ into a polar equation, and calculate r. The overlap region of the two polar plots is bound by angles where the two curves intersect, so the limits of integration depend on where these two curves intersect.
📹 Finding Area In Polar Coordinates
This Calculus 2 video tutorial explains how to find the area of a polar curve in polar coordinates. It provides resources on how to …
📹 PreCalculus – Polar Coordinates (16 of 35) Graphing Polar Equations: r=3sin3(theta), Roses
In this video I will graph polar equation r=3sin(theta), r=3sin3(theta), r=3sin5(theta), roses. Next video in the polar coordinates …
Hey everyone, in case you weren’t aware when you have symmetry over either the x-axis or y-axis and the bounds are reciprocals (ex: pi/6 and -pi/6 or pi/2 and -pi/2), you can set the lower limit of integration to 0 (so for ex: -pi/2 to pi/2 becomes 0 to pi/2) and put a two on the outside of the integral (multiplying the whole integral by two). I noticed when following along and doing the problems myself that it made the algebra at the end of the problem simpler (the zero made things easy). Hope this helps!
Love you man, legit. You’ve been teaching me from my O Levels and now I’m in college, I genuinely wish I can donate to your patreon if I ever have the opportunity to do so. For now, take my undying gratitude for shining light into the minds of so many, I hope all the good you’ve done with these articles comes back to you a hundred fold.
Professor Organic Chemistry Tutor, thank you for a fantastic article/lecture on Finding Areas in Polar Coordinates in Calculus Two. Finding the Area of a Polar Curve in Polar Coordinates is not a difficult task; However, the real problem is finding the correct limits of Integration when computing the Area. This is an error free article/lecture on YouTube TV with the Organic Chemistry Tutor.
If you’re working in radians an easier way (in my opinion) to find the first leaf is by taking the equation 3sin(k*theta), remove the 3, and set the rest of the equation equal to 1. You can take the inverse of 1 to get pi/2 and then divide the k value to get the angle where the first leaf is. also by ‘easy’ I mean that in retrospect as to why he randomly gets 90 degrees and divides the k value. this method makes sense to me personally because I can see where the numbers come from. works for degrees too in case you’re wondering.