Conics and Trigonometry

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Overview

Where will a cannonball land after firing? How does a harmonograph create art? What musical notes will produce a particular sine curve? Through motivating questions and interactive sliders, you’ll learn trigonometry and conics without relying on memorization.

By the end of this course, you’ll be a master in geometric shape equations, graphing an object’s motion, combining trigonometric identities, and identifying the perfect time to invest.

Topics covered

• Circles and Ellipses
• Exponential Growth
• Hyperbolas
• Limacons
• Logarithms
• Parabolas
• Polar Coordinates
• Sine and Cosine
• Tangent and Secant
• The Unit Circle
• Trigonometric Identities
• Wave Frequency

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1. 1

Introduction

Apply the power of experiment to learn about topics including conic sections, trigonometry, and polar coordinates.

1. Exploring the Sine

Start your study of trigonometry with this exploration of the sine function.

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2. Circles to Polar

Take the equations for circles and translate them into the language of a new type of coordinate system.

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3. Orbits

Stretch circles into ellipses and learn how they are applied to model planetary motion.

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2. 2

Conic Sections

Slice a cone to get one of these!

1. Introduction to Conic Sections

Strengthen your intuition for conic sections and explore the parabola as a special case of conic slices.

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2. Circles

Practice moving circles around the coordinate plane.

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3. Ellipses

Stretch circles into ellipses and understand the relationship between an ellipse's foci and its function.

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4. Parabolas

Learn another way to define a parabolic curve using a focus point and directrix line.

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5. Hyperbolas

Cut the cone vertically to get this strange set of conic sections.

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3. 3

Periodic Motion

Herein you'll play with rotations, cycles, and the beginnings of trigonometry.

1. Mirrors and Lenses

What happens when mirrors are shaped like parabolas?

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2. Projectile Motion

Study and control the paths of flying projectiles.

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3. Pendulums I

Learn about some of the fundamental properties of pendulums.

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4. Pendulums II

Let your pendulums swing in two dimensions and see how conic sections and trig explain what's going on!

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4. 4

Trigonometry

Apply the power of the unit circle to graph trigonometry functions and combine them together.

1. Unit Circle Trigonometry

Learn where all of the different trigonometric functions come from.

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2. Frequency and Phase Shift

Explore the basic attributes of waves.

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When you add two sine functions, sometimes it makes a mess and other times it makes just another sine.

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4. Graphing Other Trig Functions

Practice doing calculations with the more unusual trigonometry graphs.

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5. Sum and Difference Formulas

Derive a formula that's fundamental to the behavior of trigonometry.

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5. 5

Polar Graphs

Plot on a circle rather than a grid for some spectacular graphs.

1. Polar Intro

Explore a new method of graphing that uses angle and distance as the two independent variables.

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2. Basic Polar Flowers

Make flowers using sine and cosine.

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3. More Flowers

Build up your skills with polar graphing by creating and understanding more complex flowers.

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4. Cardioids and Limacons

Explore another special case — polar graphs that look like hearts and beans.

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5. Polar Problem Solving

Strengthen your skills by solving some challenging polar graphing problems.

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6. 6

Exponents and Logarithms

Keep on multiplying!

1. Exponential Growth

See what "growing exponentially" actually means.

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2. Changing the Base

What happens to the equation and the graph when you change the base?

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3. Exponential Arithmetic

Manipulate and simplify combinations and transformations of exponential functions.

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4. Financial Investing

Apply exponential functions to the world of money.

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5. Logarithms

Take the inverse of an exponent and you'll get something called a log.

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6. Log Arithmetic

Learn arithmetic shortcuts and practice adding, subtracting, and multiplying logarithms.

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