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Grades 9/10/11 Measurement, Geometry, and Trigonometry
Pythagorean Theorem. Measurement of 2D figures and 3D solids. Optimization. Geometric relationships. Triangle trigonometry. Angles in standard position and trigonometric identities.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
Units
Unit 1: The Pythagorean Theorem, Measurement, and Optimization
Unit 2: Geometric Relationships
Unit 3: Trigonometry
Unit 4: Angles in Standard Position and Trigonometric Identities
This lesson introduces angles drawn in standard position in order to extend our understanding of trigonometric ratios beyond acute angles.
In this lesson, we connect angles in standard position to their related acute angles to evaluate trigonometric ratios and find angles. We will also relate negative angles and angles greater than \(360^\circ\) to their coterminal angles between \(0^\circ\) and \(360^\circ\).
This lesson continues our work with trigonometric ratios focusing on special angles where use of a calculator is not needed.
For an acute right triangle, there are six possible ways to make a ratio using two side lengths. In this lesson, we will learn to work with the reciprocal trigonometric ratios and learn about how they behave.
We will identify the fundamental trigonometric identities and learn how to apply these to prove other identities.
All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.
This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.