At the end of the session,

the students are expected to: a. Differentiate the reciprocal identities and quotient identities of trigonometric function values, and A Semi-Detailed Lesson

with Technology Integration in MATH IV Berico, Joimari C.

Valles, Clarisse Anne C. Learning Objectives b. Solve the reciprocal identities and quotient

identities involving the six trigonometric functions. Subject Matter * Topic: Reciprocal Identities and Quotient Identities * Reference: Advance Algebra, Trigonometry and Statistics * Author: Soledad, Jose-Dilao et. al., pgs. 195-200 * Materials: Interactive Media Review * What is the domain of the function sine? cosine? tangent? * What is the range of the function sine? cosine? tangent? * What is the Y-intercept of the function sine? cosine? tangent? * What are the relationships among sine, cosine and tangent? Motivation Discussion r y x x r y where: cos θ sin θ 1 Therefore: * cos θ = x * sin θ = y

* tan θ = __ y x * csc θ = __ r y * sec θ = __ r x * cot θ = __ x y , x ≠ 0 , x ≠ 0 , y ≠ 0 , y ≠ 0 Furthermore: From the given equations, note that: * csc θ = * sec θ =

* tan θ = r x y x 1 y 1 sin θ 1 x r 1 cos θ cot θ x y r y = = = 1 = 1 = 1 = 1 Hence we have the following reciprocal identities: * csc θ = sin θ 1 * sec θ = cos θ 1

* tan θ = cot θ 1 or or or sin θ = 1 csc θ cos θ = 1 sec θ cot θ =

tan θ 1 or or or sin θ • csc θ = cos θ • sec θ = tan θ • cot θ = 1 1 1 Also from the definition we have, tan θ = y x = y r x r = sin θ cos θ , cos θ ≠ 0 And since tangent and cotangent are reciprocal functions, we have, cot θ = cos θ sin θ , sin θ ≠ 0 We therefore have the following Quotient Identities: tan θ = sin θ cos θ cos θ ≠ 0 , cot θ = cos θ sin θ , sin θ ≠ 0 Ex. 1. sin θ • sec θ sin θ • cos θ 1 = sin θ cos θ = tan θ Ex. 2. csc θ • cos θ • cos θ 1 = sin θ cos θ = cot θ sin θ Ex. 3. csc θ • tan θ = = = sec θ sec θ csc θ tan θ tan θ 1 cos θ 1 sin θ sin θ cos θ tan θ = tan θ = tan θ = = Simplify the following: sec θ csc θ 1. 2. 3. sin θ sec θ • csc θ tan θ ÷ sin θ sec θ 4. 5. csc θ • cos θ Directions: Find a partner and solve the

following in a one whole sheet of paper. sec θ cot θ ÷ 1. 2. sec θ csc θ • 3. tan θ csc θ • Reinforcement Read about the Pythagorean Identities. Assignment: Evaluation BYE!

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