This lesson will provide information that will prove the concept of sine and cosine is equal to the complementary angles of a right triangle. The lesson will examine the proper techniques for writing trigonometric ratios. The lesson will enhance background knowledge of proportions as well as use the terminology of means and extremes.
This lesson results from the ALEX Resource Gap Project.
This video will be used to re-enforce the relationships between the sides and angles in special right triangles. The video has a catchy song that will help students remember the relationships.
This activity results from the ALEX Resource Development Summit.
In this Desmos activity, students are guided through a series of questions to verify the relationships between the sides and angles of a 30°-60°-90° right triangle and a 45°-45°-90° triangle. This is intended to be a during activity for a lesson on discovering and applying relationships in similar right triangles.
In this Desmos activity, students will explore the special relationships between the sides of a 30-60-90 triangle and a 45-45-90 triangle. This is intended to be a before activity for a lesson on the relationships of special right triangles and their connection to trigonometry.
This video takes a classic trigonometry problem and brings the abstract into a real-life scenario. This would demostrate the problem in a way that would spark student interest in the subject matter. This video from Regents Review 2.0 uses a trigonometry equation to determine the height of a flagpole located in front of the school. Regents Review materials are designed to help high school students prepare for New York State's Regents exams.
Students begin the study of trigonometry in the final topic of the module. The emphasis in the module on side length relationships within similar triangles (Topic C) and the specific emphasis on right triangles (Topic D) help set the foundation for trigonometry. Lesson 25 is the last highlight of the side length ratios within and between right triangles. Students are guided to the idea that the values of the ratios depend solely on a given acute angle in the right triangle before the basic trigonometric ratios are explicitly defined in Lesson 26 (G.SRT.C.6). After practice with ratios labeled as (Lesson 21) and (Lesson 25), students are introduced to the trigonometric ratios sine, cosine, and tangent (G-SRT.C.6) in Lesson 26. Students examine the relationship between sine and cosine in Lesson 27, discovering that the sine and cosine of complementary angles are equal (G-SRT.C.7). They are also introduced to the common sine and cosine values of angle measures frequently seen in trigonometry. Students apply the trigonometric ratios to solve for unknown lengths in Lessons 28 and 29; students also learn about the relationship between tangent and slope in Lesson 29 (G-SRT.C.8). In Lesson 30, students use the Pythagorean theorem to prove the identity and also show why. In Lessons 31–33, students study the application of trigonometry to determine area and solve for unknown lengths using the laws of sines and cosines (G-SRT.9, G-SRT.10, G-SRT.11). Finally, in Lesson 34, students learn how to determine the unknown measure of an angle of a right triangle. Students are introduced to the trigonometric functions and These inverse functions are taught formally in Algebra II. For now, students should understand the meaning of and how to use and to determine unknown measures of angles.
