Education Technology

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.

    Read activities in advance.

    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.