Exploring the Sine
Start your study of trigonometry with this exploration of the sine function.
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.
Apply the power of experiment to learn about topics including conic sections, trigonometry, and polar coordinates.
Start your study of trigonometry with this exploration of the sine function.
Take the equations for circles and translate them into the language of a new type of coordinate system.
Stretch circles into ellipses and learn how they are applied to model planetary motion.
Slice a cone to get one of these!
Strengthen your intuition for conic sections and explore the parabola as a special case of conic slices.
Practice moving circles around the coordinate plane.
Stretch circles into ellipses and understand the relationship between an ellipse's foci and its function.
Learn another way to define a parabolic curve using a focus point and directrix line.
Cut the cone vertically to get this strange set of conic sections.
Herein you'll play with rotations, cycles, and the beginnings of trigonometry.
What happens when mirrors are shaped like parabolas?
Study and control the paths of flying projectiles.
Learn about some of the fundamental properties of pendulums.
Let your pendulums swing in two dimensions and see how conic sections and trig explain what's going on!
Apply the power of the unit circle to graph trigonometry functions and combine them together.
Learn where all of the different trigonometric functions come from.
Explore the basic attributes of waves.
When you add two sine functions, sometimes it makes a mess and other times it makes just another sine.
Practice doing calculations with the more unusual trigonometry graphs.
Derive a formula that's fundamental to the behavior of trigonometry.
Plot on a circle rather than a grid for some spectacular graphs.
Explore a new method of graphing that uses angle and distance as the two independent variables.
Make flowers using sine and cosine.
Build up your skills with polar graphing by creating and understanding more complex flowers.
Explore another special case — polar graphs that look like hearts and beans.
Strengthen your skills by solving some challenging polar graphing problems.
Keep on multiplying!
See what "growing exponentially" actually means.
What happens to the equation and the graph when you change the base?
Manipulate and simplify combinations and transformations of exponential functions.
Apply exponential functions to the world of money.
Take the inverse of an exponent and you'll get something called a log.
Learn arithmetic shortcuts and practice adding, subtracting, and multiplying logarithms.