Area Under Sine (draggable)

Observe the definite integral of sine, or the area between the function sin(x) and the x axis, and how it changes between different bounds by dragging the boundaries, a and b. What happens to the area when the interval is 2Π? Why?

Tags: Calculus, Defininte-Integral, Sine, Draggable

Function Composition

Define g(x) and h(x).  Now try and define f(x) so that f(g(x)) = h(x).

Tags: function, function-composition

Function composition challenge 1

Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: function-composition, algebra-2

Function composition challenge 2

Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: function-composition, algebra-2

Function composition challenge 4

Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: function-composition

Function composition challenge 5

Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: Function-composition, trigonometry

Function composition challenge 3

Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: function-composition, algebra-2

Circle Proof

This is the first app ever on Euclid’s Muse! It provides a draggable diagram to help illustrate a mathematical proof. This proof was discovered when modeling the Twisted Savonius style wind turbine from a top view. The full proof can be found here.

Tags: Proof, circles, draggable, real-world, savonius

Function composition challenge 6

Find f(x) such that f(sin(x)) matches the mystery curve.

Tags: function-composition, trigonometry

Function Product Challenge 1

Can you define f(x) so that the red curve lies on top of the grey one?

Tags: functions, function-products, trigonometry