# Search Results for “Basic-Constructions”

##### Basic Unit Circle

This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.##### Basic Derivatives

Drag the point to see how the slope of the line relates to the**x**value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the

**x**and

**y**coordinates? The slope of the line can also be represented in terms of

**x**; can you figure out what this representation is? This representation is the derivative

*of the entire function*, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of

**F(x)**=

**F’(x)**, although there are many other notations as well.