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
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 \(x\).