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我想問maths的functions.....

發問:

Given the function p(x) = cos(x°+30°) question: find the value of [p(11)]2+ [p(12)] 2+…+[p(19)] 2 (leave the answers in surd form)

最佳解答:

[p(11)]2+ [p(12)] 2+…+[p(19)] 2 = cos2 41°+ cos2 42° + cos2 43° + cos2 44° + cos2 45° + cos2 46° + cos2 47°+ cos2 48° + cos2 49° = cos2 41° + sin2 ( 90 – 49 )° + cos2 42° + sin2 ( 90 – 48 )° + cos2 43° + sin2 ( 90 – 47 )° + cos2 44° + sin2 ( 90 – 46 )° + cos2 45° = 1 + 1 + 1 + 1 + ( √2 / 2 ) 2 = 4 + 1 / 2 = 9 / 2

其他解答:

Given the function p(x) = cos(x°+30°) question: find the value of [p(11)]2+ [p(12)] 2+…+[p(19)] 2 [p(11)]2+ [p(12)] 2+…+[p(19)] 2 = cos2(11+30) + cos2(13+30) + cos2(15+30) + cos2(17+30) + cos2(19+30) = cos241 + cos243 + cos245 + cos247 + cos249 = sin2(90-41) + sin2(90-43) + cos245 + cos247 + cos249 = sin2(90-41) + sin2(90-43) + cos245 + cos247 + cos249 = sin249 + sin247 + cos245 + cos247 + cos249 = (sin249 + cos249) + (sin247 + cos247) + cos245 = 1 + 1 + (√2 / 2)2 = 2.5
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