Investigation: Trigonometry and the Pythagorean Identity

Suggested Grade Level: Grade 9 - 12 Suggested Duration: 45 - 60 minutes

This mathematical investigation is an inquiry-based task to discover the trigonometric Pythagorean identity and verify and prove the validity of the identity in grades 9 to 12.

This investigation is also designed as IB MYP Criterion B tasks for MYP 5, including the assessment rubric with a task-specific clarification, and the answer key to facilitate marking and grading for teachers.

1. The Pre-task can be done as the first part of the task, or previously as an in-class or at-home assignment.
2. Prior Knowledge required for the task
   1. Definition of the three basic trigonometric ratios (sin, cos, tan).
   2. The exact value of the sine and cosine of the common angles (0º, 30º, 45º, 60º, 90º) without the use of a calculator. They can be provided to students if they don’t know them, yet).
   3. It would be helpful and recommended to be familiar with the unit circle.
3. The IB MYP 5 Assessment Rubric is provided with a suggested task-specific clarification to facilitate implementation in the IB MYP.
4. Calculator is not required to complete the task (recommended without a calculator).
5. An answer key with expected answers is provided including a task-specific clarification for implementation as a MYP Criterion B task. However, it can equally be used as a stand-alone inquiry-based activity for any grade level and curriculum.