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Lesson plan

# Lesson 2: Revisiting Right Triangles

teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7

# Lesson 2: Revisiting Right Triangles

The purpose of this lesson is for students to recall how to determine the value of the cosine, sine, and tangent of an angle for a right triangle. This lesson builds upon the work in the previous lesson and incorporates the right triangle trigonometric ratios students encountered in a previous course.

Later in this unit, students transition to thinking of cosine and sine as functions of an angle rather than as just a way to identify ratios of sides in a right triangle. This lesson helps prepare students to make that transition by establishing how to conceptualize points in quadrant 1 as a vertex of a right triangle where the origin and a point on the $$x$$-axis are the other vertices and the right angle is on the $$x$$-axis. Using the structure of the coordinate plane this way, students identify the coordinates of the triangle vertex in quadrant 1 as the cosine and sine of the angle at the origin when the hypotenuse is 1 unit (MP7).

Lesson overview

• 2.1 Warm-up: Notice and Wonder: A Right Triangle (5 minutes)
• 2.2 Activity: Recalling Right Triangle Trigonometry (15 minutes)
• 2.3 Activity: Shrinking Triangles (15 minutes)
• Includes "Are you Ready for More?" extension problem
• Lesson Synthesis
• 2.4 Cool-down: From Coordinates to Cosine (5 minutes)

Learning goals:

• Comprehend that coordinates for a point 1 unit away from the origin in quadrant 1 can be represented by $$(\cos\left(A\right),\sin\left(A\right))$$ where $$A$$ is the angle the point makes with the $$x$$-axis.
• Recall definitions for cosine, sine, and tangent of an angle in a right triangle.

Learning goals (student facing):

• Let’s recall and use some things we know about right triangles

Learning targets (student facing):

• I understand how to use trigonometry to express the coordinates of a point in quadrant 1 that is 1 unit away from the origin.

Standards:

• This lesson builds on the standard: CCSS.HSG-SRT.CMO.G.SRT.C
• This lesson builds towards the standards: CCSS.HSF-TF.A.2MS.F-TF.2CCSS.HSF-TF.C.8MS.F-TF.8

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