HW_1_2 - -= 6 3 2 1 A [ ] -= 2 1 5 2 3 3 3 2 1 B [ ] --= 8...

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CE 221 Due Wednesday May 18, 2011 1. Proof the following trigonometric identity: a a a Tan 2 tan 1 tan 2 ) 2 ( - = 2. Proof that sin(a+b) = [sin(a)][cos(b)] + [cos(a)][sin(b)] 3. Proofs that for any triangle, the following ratios are equal (the sin law). AB/Sin(c) = AC/Sin(b) = BC/Sin(a) A C B a b c 1
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4. Proof the following trigonometric identity: ) 2 ( 1 ) 2 ( 1 ) 45 ( 2 a Sin a Sin a Tan - + = + 5. Find the magnitude of the resultant force F of the given 45 and 55 pound forces. 35 o 60 o 6. Proof the following trigonometric identity Sin 2 (a) + cos 2 (a) = 1 7. Proof that the sum of the interior angles of a triangle is 180 o . 2 55 lb F A B C 45 lb
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8. Proof that the sum of the interior angles of a hexagon (6 sided) is 720 o . 9. Proof that cos(a + b) = [cos(a)][cos(b)] – [sin)a)][sin(b)] 10.Proof that for any triangle, the following relationship is true BC 2 = BA 2 + AC 2 - 2(BA)(AC)(cos(a)) B E 3 A C D F A B C
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11. Obtain the determinants of the following matrices. [ ]
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Unformatted text preview: -= 6 3 2 1 A [ ] -= 2 1 5 2 3 3 3 2 1 B [ ] --= 8 6 1 7 4 2 1 5 3 2 1 1 1 C 12. Obtain [A] T for the given [A] matrix. [ ] ---= 5 6 2 4 3 2 2 3 4 A 13. Obtain the inverse [B]-1 of the given [B] matrix. [ ] -= 4 2 2 6 4 2 2 B 4 14. Obtain matrix [C] by multiplying matrices [A] and [B]. [ ] [ ] [ ] - -= = 5 6 4 2 3 2 * 4 1 6 5 2 * B A C 15. Solve the following equations using matrix operation. Verify your answer using the traditional solution of three simultaneous equations. X + Y + Z = 3 2X + 0.5Y + Z = 2 4X Y Z = 7 5...
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This note was uploaded on 02/03/2012 for the course CE 221 taught by Professor Buch during the Summer '08 term at Michigan State University.

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HW_1_2 - -= 6 3 2 1 A [ ] -= 2 1 5 2 3 3 3 2 1 B [ ] --= 8...

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