The Polar Quartet

The Polar Quartet Napa Valley College

Welcome!

Aaron, Tonie, Vivienne, and John-Michael are really excited to present everyone with our digital handout! We've adapted our presentation and content of Chapter 11 Parametric Equations and Polar Coordinates to create the ultimate study guide that can be viewed from all of your devices: desktops, notebooks, tablets and smartphones. Included in this digital handout are conceptual explanations of all the major content inside Chapter-11; from Parametrizations to Polar Graphs. We're also very proud to be able to include detailed voiceover solutions for the study guide problems that were created for everyone to practice on their own time; all narrated by members on our team.

We hope you utilize this tool in your Arsenal of studies and of course In your endeavor to pass the final

Spring 2015

ParametErizations

The defining characteristic of a parametric are that the common variables we deal with: "x and y" are now both dependent on a new variable: "t."

Using parametrics gives us the advantage to express what would be a complex piecewise functions with a more simple and precise parametric equation.

Parametrics and Calculus

Be cautious not to switch the derivative of y with the derivative of x

Note: that you're finding the derivative of dy/dx, not dy/dt

It's beneficial to proceed with the algebra content inside the radical first before proceeding to integrate

Polar CooRdinateS

Rather interesting is that when graphing polar coordinates you start with the angle before the ray length

Remember that r=f(θ)

More Polar graphs

Yes that's an egg

Solutions

The next section is designed to work in conjunction with the handout you received to practice your skills and prep for the upcoming final. Don't worry if you misplaced the physical handout, the original problems are here as well. Along with the solutions, you will be presented with a link to a detailed voiceover of the solution, just in case you didn't work to the same solution as our team did.

We hope you enjoy the narrations!

Problem 1

Hint: Make sure you didn't flip dy and dx

Detailed Voiceover Solution Guide Problem 1

Problem 2

Hint: +3 and -2 are translations, not transformations

Detailed Voiceover Solution Guide Problem 2

Problem 3

Hint: you can't just integrate the rose from 0 to 2π

Detailed Voiceover Solution Guide Problem 3

Problem 4

Hint: Make sure your algebra is methodical when finding the derivative

Problem #4 solution

Detailed Voiceover Solution Guide Problem 4

That's the End of our detailed voiceover solution guides, but we did include one last thing for fun. If you've mastered the study guide CheCk out the Last video Below.

This integral can only be done by utilizing polar equations.

Gaussian Integral Detailed Narrated VoiceOver Guide

WE HOPE YOU LOVE THIS DIGITAL HANDOUT AS MUCH AS WE LOVED CREATING IT!

Created by John-Michael Laurel, Tonie Scroggin, Aaron Koford, and Vivienne OoI.

CALCULUS 2 SPRING 2015 PROFESSOR BYNUM

Professor Bynum, Tonie, John-Michael, Vivienne, Aaron

Appreciate

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