# Activities

• • • ##### Subject Area

• Math: Precalculus: Series
• Math: Precalculus: Trigonometry (Triangle and Circular Functions)

• ##### Author 9-12
College

55 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™ CAS

3.0

• ##### Report an Issue

Exploring the Law of Sines and Taylor Polynomials

#### Activity Overview

This activity is the second part of an activity that allows students to explore the Law of Sines. While exploring that relationship, students investigate the relationship between the side of a triangle and the angle opposite that side. Students collect data for different triangles and graph the ratio of the sin A:A. That data is graphed and the students try to fit a polynomial to the curve (a quadratic). Then students explore Taylor Polynomials for the sign curve.

#### Before the Activity

Do the Law of Sines activity.

#### During the Activity

The students will collect data on the ratio of the sin A: A and then fit a polynomial curve to the graph. They will first try to fit a quadratic curve and find the results actually quite good. They will need to think carefully about the quadratic function that they will be using. Then introduce the students to the Taylor Polynomial command on the TI Nspire CAS. Have the students try fitting only a first degree polynomial then third degree, etc. As they increase the number of terms the better the curve approximates the ratio. The students will have not estimated a trigonometric function with a polynomial. Use the attached CAS TNS file to run the activity.

#### After the Activity

Encourage the students to summarize what they have learned from completing the activity.