Lesson Plan in Mathematics Trigonometric Identities PDF

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Summary

I. Objectives: At the end of the lesson the students should be able to: a. identify the Eight Fundamental Identities; b. discuss the Eight Fundamental Identities; c. simplify trigonometric expression; and d. prove trigonometric function.II. Learning Task: Topic: Trigonometric Identities Sub-topic: E...

Description

I.

Objectives: At the end of the lesson the students should be able to: a. identify the Eight Fundamental Identities; b. discuss the Eight Fundamental Identities; c. simplify trigonometric expression; and d. prove trigonometric function.

II.

Learning Task: Topic: Trigonometric Identities Sub-topic: Eight Fundamental Identities References: Plane Trigonometry by Divina C. Chavez Materials: tan-sin-cos hexagon, chalk and board Values: Show neat and orderly proof. Learning Strategies

III.

Teacher’s Activity A. Daily Classroom Routines 1. Greetings “Good morning class.” 2. Prayer “Before we formally start, let us all stand up and feel the presence of our Lord. Harol, please lead the prayer.”

Students’ Activity

“Good morning, Sir Ace!”

(Harol will go in front and will lead the prayer.)

3. Classroom Management “Before you take your seats, please kindly pick up the pieces of paper in your respective areas and arrange your chairs properly. Thank you.”

“Yes Sir!” (The students will clean their areas and will arrange their chairs properly.)

4. Checking of Attendance “Class monitor, how many absentees do we have today?”

(The class monitor will say how many absentees they have for the day.”)

“That’s good. I know you don’t want to miss the continuation of our lesson today.” B. Refreshing Mind (Motivation) “Before we formally start the class, let’s first have a game. The class will

be divided into two. Each group will form a circle with their group mates. You will be given pieces of paper that contained your task which is to prove that 2 = 0/0. Each group will be given five minutes to conceptualize their answer. The group that will get the answer correctly will get an additional point on the next activity. Are you ready?”

“Yes Sir!”

“You may now go with your group. (The students will proceed to their group and Five minutes starts now.” will do the activity.) C. Establishing the Background (Presentation) “So class, we will discuss about the Trigonometric Identities. Trigonometric Identities means a relation involving trigonometric functions which is valid for all values of the angle for which the functions are defined. The fundamental identities where all other identities are derived from classified into “Yes Sir!” reciprocal, quotient and Pythagorean. Am I clear?” D. Discussion “So let’s start. Our topic for today is the Eight Fundamental Identities. So let us first discuss the Reciprocal Identities. Do you have any idea on what does the word “Reciprocal” means?” “Yes, Lara?” “Exactly. Very good Lara. So that is somewhat related with our first set of identities. There are three identities

(The class will raise their hands.) “Reciprocal something.”

means

the

opposite

of

under Reciprocal Identities and these are: 1. csc x = ↔ sin x csc x = 1 2. sec x = ↔ sec x cos x =1 3. cot x = ↔ tan x cot x = 1 The next set of identities is under the Quotient Identities. Do you have any idea on does the word “Quotient” means?” “Yes, Rush?” (The class will raise their hands.) “You got it right, Rush. So that is somewhat related with our second sets of identities. There are two identities under the Quotient Identities and these are: 4. tan x = 5. cot x =

“Quotient is the answer to a two expressions that were divided by each other.”

The last set of identities is under the Pythagorean Identities. Do you have any idea on what is the Pythagorean Theorem?” “Yes, Rezel?” “Very good, Rezel. So that is somewhat related with our last sets of identities. There are three identities under the Pythagorean Identities and these are: 6. 7. 8.

sin2x + cos2x = 1 sec2x + tan2x = 1 csc2x + cot2x = 1

These fundamental identities can be used in transforming expressions into

(The class will raise their hands) “Pythagorean Theorem tells that c2=a2+b2”

other forms. To prove trigonometric equations, consider the more complicated side and manipulate it until it assumes the form of the other sides. Are we clear?” “So for you to understand it more, I have here some examples. These are: 1. cosxtanx = sinx “Yes sir!”

= cosx = sinx = sinx 2.

+ = 2sec2x In this case we will transform the left side into the exact form of the right. 2sec2x = + = = = = 2()2 = 2(secx)2 2sec2x = 2sec2x

Do you have clarifications?”

questions

or

“So let us test your knowledge. We will have an activity.”

“None, sir.”

E. Application “So here’s the mechanics, the same group as the previous activity, the class will be divided into two. Each group must have one representative. A trigonometric equation will be shown to you. Your representative must prove that the given equation is equal. They are allowed to have a brainstorming with their group mates and once their answer was already finalized, the representative will go directly to the board and write their answer together with their solution. The first group that will write the correct answer will be the winner. The equation is: sec4x – sec2x = tan2xsec2x “Are you ready?” “So let’s start our activity.”

“Yes, sir.” (The students will start the activity.)

F. Evaluation “Class, please get a one whole sheet of paper and prove the following identities. 1. = tanx 2. 1-- = sinx

(The students will get a sheet of paper and will start answering.)

3. Tanxcotxtan2x = tan2x” G. Assignment “Please pass your one whole sheet of paper and bring out your book. Answer the activity in pages 66-68. Write your answer in your notebook. We will check your assignment tomorrow. Now before we ends, do you have questions, violent reactions, comments or additional information that you have in your mind?”

“None, sir.”

“So let’s call it a day. Goodbye class.” “Goodbye, sir!”...