T09_Analytic_Trigonometry

# T09_Analytic_Trigonometry - PMC 0045 Pre-Calculus for...

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Unformatted text preview: PMC 0045 Pre-Calculus for Engineering Foundation in Engineering ONLINE NOTES Topic 9 Analytic Trigonometry FOSEE , MULTIMEDIA UNIVERSITY (436821-T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/ Mathematics Department (MD) Centre for Foundation Studies and Extension Education (FOSEE) PMC0045 Pre-Calculus for Engineering Topic 9 TOPIC 9: ANALYTIC TRIGONOMETRY References : 1. Sullivan, M. (2002), Algebra & Trigonometry , 6 th Ed., Prentice Hall. 2. Blitzer, R., Goh Wei Wei, et.al. (2005), Algebra & Trigonometry , Prentice Hall. Objectives: 1. Understand the characteristics of all trigonometric functions. 2. Be able to sketch and apply the shifting techniques to all trigonometric functions. 3. Understand the characteristics of a sinusoidal function and be able to find the period and amplitude of this function. 4. Understand the characteristics of all inverses of trigonometric functions. 5. Be able to find the exact value of expressions involving inverse trigonometric functions. 6. Establish the identities. 7. Solve a trigonometric equation. Contents: 9.1 Inverse Trigonometric Functions 9.2 Verifying Trigonometric Identities 9.3 Sum and Difference Formulas 9.4 Double-Angle and Half-Angle Formulas 9.5 Product-to-Sum and Sum-to-Product Formulas 9.6 Trigonometric Equations 9.1 INVERSE TRIGONOMETRIC FUNCTIONS Recall : If the function is one-to-one, it will have an inverse. The Inverse Sine Function Sine function is not one-to-one, but if we restrict the domain of y = sin x to the interval - π π 2 2 , , the restricted function y x x =- ≤ ≤ sin , π π 2 2 is one-to-one function, and hence, it has an inverse i.e. , y x x y = ⇒ =- sin sin 1 where - ≤ ≤ π π 2 2 y and - ≤ ≤ 1 1 x Example : (Finding the exact value of an Inverse Sine Function) Find the exact value of sin ( )-- 1 1 . ______________________________________________________________________________________ Mathematics Dept 2/ 7 PMC0045 Pre-Calculus for Engineering Topic 9 Solution : Let θ =-- sin ( ) 1 1 . Then, we seek the angle θ , - ≤ ≤ π θ π 2 2 , whose sine equals -1 : sin , θ π θ π = -- ≤ ≤ 1 2 2 θ π = - 2 , (since the only angle within the interval whose sine = -1 is - π 2 )....
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T09_Analytic_Trigonometry - PMC 0045 Pre-Calculus for...

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