Tutorial 8 Trigonometric Functions and Basic Differentiation.pdf - FAM0015/FBM0025 QA1 2019 TUTORIAL 8 CHAPTER 4 and CHAPTER 5 TRIGONOMETRIC FUNCTIONS

Tutorial 8 Trigonometric Functions and Basic Differentiation.pdf

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FAM0015/FBM0025 QA1 2019 Open 1 PREPARED BY WSWMP MODIFIED MAY 2019 TUTORIAL 8 : CHAPTER 4 and CHAPTER 5 TRIGONOMETRIC FUNCTIONS Find the value of each of the other five trigonometric functions for an angle ? , given the information indicated below. 1. sin ? = 3 5 and cos ? < 0 2. tan ? = − 4 3 and sin ? < 0 3. cos ? = − √5 3 and cot ? > 0 4. cos ? = 3 5 and 270° < ? < 360° 5. tan ? = 1 4 and 0° < ? < 90° 6. sec ? = −4 and 90° < ? < 180° Verify the given identities. 1. cos 2 ? − sin 2 ? = 1 − 2 sin 2 ? 2. (csc ? − 1)(csc ? + 1) = cot 2 ? 3. sin 2 ? cos ? + cos ? = sec ? 4. sin ? 1 − cos 2 ? = csc ? 5. cos 2 ? − sin 2 ? sin ? cos ? = cot ? − tan ? 6. csc ? − sin ? 1 + cos ? = cot ?
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FAM0015/FBM0025 QA1 2019 Open 2 PREPARED BY WSWMP MODIFIED MAY 2019 Find the derivative of the following functions 1. ? = 5 4 ? 4 5 2. ? = ? 4 − 2? 2 + 5 3. ? = 2? 3 − 4? 2 + 3 ? 4. ? = ? 3 + 2? 2 + ? − 1 ? 5. ? = 4? 4 − 3? 5 2 + 2 6. ? = 3? − 5√? 7. ? = 5? −1 + 4? −2 8. ? = − 1 3 (? −3 − ? −6 ) 9. ? = 2?(? 2 + 1) 10. ? = (2? + 3)(3? − 4)
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