DETAILED LESSON PLAN IN TRIGONOMETRY Prepared by: Jetly M. Remilla Teacher applicant I. OBJECTIVES At the end of the lesson, the learners should be able to: 1. Define the six trigonometric ratios of an acute angle of a triangle. 2. Illustrate the six trigonometric ratios of angle theta. 3. Use trigonometric ratios to solve applied problems. II. SUBJECT MATTER Topic: The Six Trigonometric Functions Reference: Solidad Jose-,Dilao and Fernando B. Orines. Advanced algebra, Trigonometry and Statistics. (Revised edition); pp. 210-216 Roland E. Larson and Robert P. Hostetler. Trigonometry(4th edition); pp. 136-142 Materials: Hunt-a-word puzzle (in manila paper), Cut- out of triangles Strategy: Discussion III. LEARNING ACTIVITIES Teacher's Activity Learners' Activity Daily Routine Good morning class Good morning Sir Roela will you lead us in prayer Roela will lead the prayer Thank you, Roela. You may now take your seat. The learners will sit down Chezca, will you kindly check who's present and who's absent for today. Review Before we proceed to our new lesson, lets have a quick review. What was our previous lesson? Thats right. So how do we convert angle measure from degree to radians and radians to degree? It's all about on how to convert Radians to degree. In converting the angle measure from degree to radians we use the Π/180 and radians to degree we use the 180/Π. Motivation Now that you know how to convert degree to radians and radians to degree, let’s have a simple game. (Showing a hunt-a-word puzzle). In one minute I want you to find the six words below. The learners will look for the words Have you found them all? Yes Sir I want the group of Luis to show us the word below. Can you stand up and box the words? The group of Luis will box the words Thank you. You may now take your seat. Lesson Proper Have you already encountered these words? Not yet Sir. Today we will be discussing the six trigonometric functions. (Showing the cut out of a triangle) We have a right triangle ABC with the right angle at C and the two legs a and b. The opposite of C which is c is The learners will listen the hypotenuse. With respect to the acute angle , side a is the side opposite to , the b would be the side adjacent to . (Showing the six trigonometric functions) There are six main trigonometric functions: Sine (sin) Cosine (cos) Tangent (tan) Secant (sec) Cosecant (csc) Cotangent (cot) These are six trigonometric functions of an acute angle. Before we find the trigonometric functions of our triangle, let us read first the definition of it. The six trigonometric functions are defined as ratios of sides in a right triangle. Their values depend only on the angle and not on any particular right triangle. A good way to remember the definitions of sine, cosine, and tangent is with the memory device soh cah toa. What is meant by soh cah toa? SOHCAHTOA. A way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent. Correct. Here is an illustration of the soh cah toa: Let us first find the sin . What is the side opposite to the angle and the hypotenuse? The side a is the side opposite to the angle the side c is the hypotenuse. To label it, we will write a/c. That is how we find the sin . Now to find cos , we need to find the side adjacent and the hypotenuse of the triangle. So how we will label the cos ? Cos = b/c Very good. In tan we need the side opposite and the side adjacent. How we will label it? Tan = a/b For the remaining three functions, these three are the opposite of the first functions. The cot is opposite to the function of tangent where the cot is side adjacent over side opposite. Who can write the label of the cot , on the board? The learners will raise his/her hand Cot = b/a In sec and csc , their opposites are the cos and sin . So our sec = c/b and the csc = c/a. Thats how we find the six trigonometric functions. We will only follow the definition of these trigonometric functions. Do you have any question? None Sir. and Application (Showing an illustrated example) √3 2 1 Let's have another example. Find the six functions of the triangle. Who would like to find the first three functions? The learners will raise his/her hand Sine = √3/2 Cosine = 1/2 Tangent = √3/1 Very good. How about the last three functions? The learners will raise his/her hand Cosecant = 2/√3 Secant = 2/1 Cotangent = 2/√3 IV. EVALUATION Find the six trigonometric functions of the triangle. 1.) 2. ) 8 3.) 10 12 13 5 17 15 6 8 V. ASSIGNMENT Memorize the six trigonometric functions we will be having a short quiz for the next meeting.
