Interactive course — Foundational Math

Conics and Trigonometry

Master trigonometry through interactive graphs and mesmerizing visuals.

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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

Interactive quizzes

28

Concepts and exercises

240+

Course map

Prerequisites and Next Steps

  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.

      1
    2. Circles to Polar

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

      2
    3. Orbits

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

      3
  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.

      4
    2. Circles

      Practice moving circles around the coordinate plane.

      5
    3. Ellipses

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

      6
    4. Parabolas

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

      7
    5. Hyperbolas

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

      8
  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?

      9
    2. Projectile Motion

      Study and control the paths of flying projectiles.

      10
    3. Pendulums I

      Learn about some of the fundamental properties of pendulums.

      11
    4. Pendulums II

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

      12
  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.

      13
    2. Frequency and Phase Shift

      Explore the basic attributes of waves.

      14
    3. Adding Sine Curves

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

      15
    4. Graphing Other Trig Functions

      Practice doing calculations with the more unusual trigonometry graphs.

      16
    5. Sum and Difference Formulas

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

      17
  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.

      18
    2. Basic Polar Flowers

      Make flowers using sine and cosine.

      19
    3. More Flowers

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

      20
    4. Cardioids and Limacons

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

      21
    5. Polar Problem Solving

      Strengthen your skills by solving some challenging polar graphing problems.

      22
  6. 6

    Exponents and Logarithms

    Keep on multiplying!

    1. Exponential Growth

      See what "growing exponentially" actually means.

      23
    2. Changing the Base

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

      24
    3. Exponential Arithmetic

      Manipulate and simplify combinations and transformations of exponential functions.

      25
    4. Financial Investing

      Apply exponential functions to the world of money.

      26
    5. Logarithms

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

      27
    6. Log Arithmetic

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

      28