Lesson 8

Sine and Cosine in the Same Right Triangle

Lesson Narrative

In a previous lesson, students built a right triangle table. Each group had a pair of complementary angles, so they began to make conjectures about cosine and sine of complementary angles before they learned the terms cosine or sine. In this lesson, students do some calculations to remind them of their previous conjectures and then prove \(\sin(\theta)=\cos(90-\theta)\).

Throughout this lesson there is a focus on precision of language. The warm-up prompts students to compare four triangles. The Which One Doesn't Belong? routine gives students a reason to use language precisely (MP6). The following activity asks students to explain how they got the same answers as their partner despite being assigned different triangles (the pairs of triangles were congruent but had different angles provided). In the final activity students write a draft of a proof, work with their group to refine the group proof, and then have a whole class discussion on how to clearly communicate ideas using words and diagrams.


Learning Goals

Teacher Facing

  • Explain the relationship between the cosine and sine of complementary angles (using words and other representations).

Student Facing

  • Let’s connect cosine and sine.

Learning Targets

Student Facing

  • I can explain why $\sin(\theta)=\cos(90-\theta)$.

CCSS Standards

Building On

Addressing

Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In