Lesson 2

Revisiting Right Triangles

Lesson Narrative

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 on 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).

Learning Goals

Teacher Facing

  • Comprehend that coordinates for a point 1 unit away from the origin in quadrant 1 can be represented by $(\cos(A),\sin(A))$ 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.

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.

CCSS Standards

Building On

Building Towards

Glossary Entries

  • period

    The length of an interval at which a periodic function repeats. A function \(f\) has a period, \(p\), if \(f(x+p) = f(x)\) for all inputs \(x\).

  • periodic function

    A function whose values repeat at regular intervals. If \(f\) is a periodic function then there is a number \(p\), called the period, so that \(f(x + p) = f(x)\) for all inputs \(x\).