Education Technology

# Activities

• ##### Subject Area

• Mathematics: Calculus: Calculus
• Mathematics: Function and Graphs: Function and Graphs
• Standard: VCE: Mathematical Methods: Mathematical Methods

Aust Senior

45 Minutes

• ##### Device
• TI-Nspire™ CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CAS
TI-Nspire™ CAS Navigator™ NC System
TI-Nspire™ Navigator™ NC System

4.0

## Square Peg in a Round Hole

#### Activity Overview

How does the magical black box produce values for sin(x)? Something as simple as a quadratic function can produce values for sin(x) with remarkable accuracy. Increase the degree of this polynomial slightly and the results are really impressive. This activity involves simple applications of the factor theorem, differential calculus and is a great launching point for the mean value theorem.

#### Objectives

Understand how values for trigonometric functions are generated.

Sketch curves associated with simple polynomials; find stationary points, and local and global maxima and minima; and examine behaviour as x approaches positive / negative infinity.

#### Vocabulary

Polynomial, degree (of polynomial), derivative, coefficient