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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.
Primary Learning Objective(s):
The student will be able to determine the sides of a right triangle.
The student will demonstrate knowledge of ratios of a right triangle for sine and cosine.
The student will compare ratios for sine and cosine for right triangles.
Additional Learning Objective(s):
The student will calculate sine and cosine values using a calculator.
The student will calculate angles given the values of sine and cosine using a calculator.
31 to 60 Minutes
Materials and Resources:
Resources for Teacher Activation and Preview
1. Basic Trigonometry video from Khan Academy www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/v/basic-trigonometry
2. Finding-Trigonometric-Ratios.pdf is PDF file worksheet in the attachments/resources section. This resource was downloaded from Kuta Software. The teacher will need to make copies for all students unless the teacher is using Google classroom.
3. Writing ratios for sine, cosine, and tangent from Khan Academy
4. PowerPoint in the attachments/resources section for the bell ringer and the exit slip
5. Worksheet for the accelerated students in the attachments/resources section. Copies need be made for students that finish early.
Students will need one sheet of paper and a pencil.
Technology Resources Needed:
Interactive whiteboard with computer/projector for the teacher and the students
iPad, Chromebooks, or MacBooks for each student for intervention (revisiting websites) and submitting classwork on Google classroom
Wi-Fi and Google classroom for all students and teacher
Calculators with trig functions for all students
The teacher must have the knowledge to show students how to use a calculator to find sine, cosine, and tangent values. All calculators are different when it comes to inputting values for angles. Casio calculators ask for the angle measure first then trig ratio. Texas Instrument calculators will need the trig ratio first then the angle measure. The teacher and students will need to experiment with the calculators to understand how each type works. The teacher will need to preview the website and activities with Khan Academy. The website and program are a great resource for teachers. The teacher will need to be ready to explain and show “means and extremes” to the students.
The students will need to understand ratios, unit rates, and proportions. The students will need knowledge of complementary angles as well as properties of a right triangle. The student should be able to use the Pythagorean Theorem to calculate missing sides of a right triangle.
From the bell ringer triangle…Draw the triangle on the smart board
Students compare ratios: sine x = cosine y
Students compare ratios: cosine x = sine y
The students have proven that the trig ratios (sine/cosine) of opposite complementary angles of a right triangle are equal.
As the students begin the assignment, place the second slide from the PowerPoint in the attachment/resources section on the smart board. Ask the students to complete the problem on their own paper and turn it in as they leave the classroom.
The teacher will assess the students as the video is playing as well as soliciting answers from students.
The teacher will make an informal assessment by grading the worksheet that is turned in or submitted through Google classroom.
The teacher can make a formal assessment by using the exit slip at the end of class. The students will be able to complete the assignment with 100% mastery. The exit slip is the second slide from the PowerPoint in the attachment/resources section.
Copy the worksheets named "Accelerated" in the attachments/resources section. These worksheets are for the students that finish early.
The students that need accommodating and extra reinforcement will receive one-on-one tutorial. Also, the teacher can pair the students with a peer tutor from the class.