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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.


  • 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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