Lesson 2: Revisiting Right Triangles
About this lesson
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 Warmup: 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 Cooldown: 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.HSGSRT.CMO.G.SRT.C
 This lesson builds towards the standards: CCSS.HSFTF.A.2MS.FTF.2CCSS.HSFTF.C.8MS.FTF.8
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