Education Technology

# Activities

• ##### Subject Area

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

9-12

60 Minutes

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

TI-Nspire™
TI-Nspire™ CAS

## Exploring Trigonometric Ratios

#### Activity Overview

• Students will calculate sines, cosines and tangents of acute angles in right triangles.
• Students will find that similar right triangles have constant trigonometric ratios.
• Students will review that similar triangles have angles that are congruent and proportional sides.

The extension goes into angles beyond 90°.

• #### Before the Activity

Teacher preparation:
Download the attached .Doc documents and the TI_Nspire document. You will need to copy the .TNS document to students; handheld before the exploration.

#### During the Activity

Classroom management tips:
Be prepared to guide students during the exploration.
Encourage students to look for patterns, make connections, and share their findings during the exploration.

#### After the Activity

• Evaluate students' conjectures written on page 4.1 on their TI_Nspire document.
• Activity extensions: Students will determine side length of right triangles by using trigonometric functions.
• Connections to other content areas to explore: trigonometric ratios can be used to measure the heights of objects, such as an eruption of a geyser that cannot be measured directly.

Use the attached "Extending Trig Ratios" to accomplish the following objectives:
• Students will use a rotating ray in a coordinate plane to define angles measuring greater than 90° and less than 360°.
• Students will define sine, cosine, and tangent for angles of any size.
• Real-world connections for the Extension: Students can use angles of rotation to determine the rate at which a skater must spin to complete a jump.
• Connections to other content areas to explore: Periodic phenomena such as sound waves can be modeled with trigonometric functions.