"I Saw the Sine"
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This lesson provided by:
Author: Morgan Boyd
Organization: Retirement

General Lesson Information
Lesson Plan ID:
35580
Title:

"I Saw the Sine"
Overview/Annotation:

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.

Associated Standards and Objectives
Content Standard(s):
Mathematics MA2015 (2016) Grade: 9-12 Geometry 20 ) Explain and use the relationship between the sine and cosine of complementary angles. [G-SRT7]

Local/National Standards:

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.

Preparation Information
Total Duration:

31 to 60 Minutes

Materials and Resources:

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

Background/Preparation:

Teacher Background

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.

Student Background

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.

Procedures/Activities:
Before:

As the students enter the classroom, the Bell Ringer should be posted on the interactive whiteboard (The bellringer can be found on the first slide of the PowerPoint located in the attachments/resources section).
Select students at random to answer the bell ringer. (Answers: Hypotenuse is 5, one leg is 3 and the other leg is 4.)
Introduce the video from Khan Academy (“Basic Trigonometry” )
The teacher can stop the video for questioning and comprehension.
During:

After the video, the teacher should introduce the saying “sock-a-tow-a” (SOH-CAH-TOA).
Show the students how to use the calculator to find sine, cosine, and tangent. Press the trig ratio key and then the angle.
Use the calculator to find the angle from the decimal form of the trig ratio. Press INV key then trig ratio key.
Explain that the letters in front stand for a particular trig ratio of the right triangle.
S – sine
C – cosine
T – tangent
O – opposite side of the given angle
A – adjacent side of the given angle
H – hypotenuse
Use the Bell Ringer and given the bottom angle to write the trig ratios in fraction form and decimal form.
3/5 and 0.6 are the Sine using the bottom angle
4/5 and 0.8 are the Cosine using the bottom angle
Show the video “Writing the ratios for sine, cosine, and tangent” .
Using the angles of a right triangle, show the students that the two angles will be acute. The sum of the two acute angles must be 90 degrees, which makes them complementary.
Using the definition of proportions, the sine of one acute angle will equal the cosine of the other acute angle
The students will make a table and compare ratios.
From the bell ringer triangle…Draw the triangle on the smart board

Sine x

4/5

Sine y

3/5

Cosine x

3/5

Cosine y

4/5

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.

After:

Assign the problems from the PDF worksheet in the attachments/resources section.
The teacher can upload the worksheet in Google classroom, then the students can access it and submit the answers.
If the teacher does not have access to technology, then he/she will need to make copies for each student.
The students will complete the worksheet for homework.
Exit Slip

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.

Attachments: **Some files will display in a new window. Others will prompt you to download.

Assessment
Assessment Strategies

Informal:

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.

Formal:

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.

Acceleration:

Copy the worksheets named "Accelerated" in the attachments/resources section. These worksheets are for the students that finish early.

Intervention:

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.

View the

Special Education resources for
instructional guidance in providing modifications and adaptations
for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.