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Homework_1___2 - CE 221 Homework 1 2 Due Wednesday 1 Proof...

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CE 221 Homework 1 & 2 Due Wednesday September 15, 2010 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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