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anonymous
 4 years ago
find the value sin36.
anonymous
 4 years ago
find the value sin36.

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DLS
 4 years ago
Best ResponseYou've already chosen the best response.0Refer this: http://www.goiit.com/posts/list/trignometryfindvalueofsin36cos181014971.htm

mayankdevnani
 4 years ago
Best ResponseYou've already chosen the best response.1sin(5x) = 16sin^5(x)  20sin^3(x) + 5sin(x). With x = 36°, we see that: sin[5(36°)] = 16sin^5(36°)  20sin^3(36°) + 5sin(36°) ==> 16sin^5(36°)  20sin^3(36°) + 5sin(36°) = sin(180°) ==> 16sin^5(36°)  20sin^3(36°) + 5sin(36°) = 0, since sin(180°) = 0. Then, if we let u = sin(36°), the equation becomes: 16u^5  20u^3 + 5u = 0. By factoring: 16u^5  20u^3 + 5u = 0 ==> u(16u^4  20u^2 + 5) = 0 ==> u = 0 and 16u^4  20u^2 + 5 = 0. However, since sin(36°) > 0 since 36° lies in Quadrant I, u = 0 is discarded. We are now left to solve: 16u^4  20u^2 + 5 = 0. (Note that this is just a quadratic equation in u^2) By the Quadratic Formula: (b^2  4ac = (20)^2  4(16)(5) = 80): u^2 = [b ± √(b^2  4ac)]/(2a) = (20 ± √80)/32 = (20 ± 4√5)/32 = (5 ± √5)/8. By taking the positive square root (again, u = sin(36°) > 0): u = √[(5 ± √5)/8] = √(10 ± 2√5)/4. At this point, we need to decide which sign we should be pick. To do this, we note that: sin^2(36°) < sin^2(45°) = 1/2. Since the positive square root gives us sin^2(36°) > 1/2 as: (5 + √5)/8 > (5  1)/8 = 1/2, we pick the negative sign. Therefore, sin(36°) = √(10  2√5)/4. http://answers.yahoo.com/question/index?qid=20110212184922AAbvfnJ
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