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Unformatted text preview: PMC 0045 Pre-Calculus for Engineering Foundation in Engineering ONLINE NOTES Topic 10 Additional Topics in 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 10 TOPIC 10: ADDITIONAL TOPICS IN 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. Solve Right Triangles. 2. Use the Law of Sines and Cosines to solve a triangle. 3. Study the area of a triangle. 4. Convert from rectangular to polar coordinates and vice versa. Contents: 10.1 The Law of Sines 10.2 The Law of Cosines 10.3 Polar Coordinates 10.4 Complex Numbers in Polar Form; De Moivre’s Theorem 10.1 THE LAW OF SINES Definition : A triangle is called oblique , if none of the angles of the triangle is a right angle. To solve an oblique triangle means to find the lengths of its sides and the measurements of it angles. Four possibilities have to be consider: 1. One side and two angles are known. 2. Two sides and the angle opposite one of them are known. 3. Two sides and the included angle are known. 4. Three sides are known. The first two cases require the Law of Sines and the last two requires the Law of Cosines. Law of Sines : For a triangle with sides a, b, c and opposite angles α β γ , , respectively sin a α β γ = = sin sin b c Example : Solve triangle with ο ο β α 8 . 81 , 32 = = and a = 42.9 cm....
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