Problem 57512. Easy Sequences 89: Double Summation of a Trigonometric Product

Created by Ramon Villamangca

Solve Later

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<div style = "text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; "><div style="block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 492.078125px 144px; transform-origin: 492.078125px 144px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">Given and angle </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">A</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; "> in radians and a positive integer </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">x</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">, evaluate the following product summation:</span></span></div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">                    </span></span><span style="vertical-align:-17px"><img 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" width="236" height="46" style="width: 236px; height: 46px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">which 'directly' translates to Matlab as:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">For example </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAASaADAAQAAAABAAAAJAAAAABLVRfgAAADDUlEQVRoBe2YW4hNURjHDyGkQe5GaVxTSjyQogmTS7yM24M3vHhyefAipXhAIVLyIJQ8KUqSEi/EvLgWHlzKPcnInXL7/af9TWuOtffsfY7pzJ6zvvqd9e21vrXOWv+9bucUCsGCAkGBoEBQIFcKdMtVb8vv7CyamA4T4SVchyb4BFVvtShwDv54kFiToaqtL6O/BRLoBpyKUlewZvIGQNXafkb+DVYWKVDH8z0wsZYWlVfNYw0j1X7TGDPiFeSbSHtiYgrd4wq6SP4YxqGZdCZmPG+c/KeOH1xHga34mkm/YJKT38bt0ebp34c+ZDXAVFBDB+AzmC3AUfkVOGuZOUl70k/bh3bgPyil37uppPUscXzrdq+TL+F0iuTF1NfzoHFtK6fTE6jcD0aBRFCDpvamKO8o6RO4CGnsNEHv/gPz0nyZJ0Z78CK4CfbiP+Kvh7JNG581Oh//O2ipZTWJae2Uky7M+sXEa/Y8Tvj+DXFtpv1Zopmzz2lEx+Vm5zmtqxkwNm1wQpxe2tuE8riiERTo0jgONsJcMPuAMx5KabeljRl82pvXUZmn/adlAJ4PTZB1oH3XxrbKE5c6qxeRurWqMe0rXcl2MRgTabtvYNrI0piuCnb0z0xTIUcxF5y+DnT8VleDT2PagwZHgcNJtaYfRc9ZEs3C+iwVYmL1O+xSTFnW7GtU+A2aMA+zVrb4JTi6Kx0Cm5arrTBjWsnTLa6rQ51xzfEFafNKsmEU3oXjoLWrO47qHIM1oFvrQdgCzdCeVfp08/VPL1z3vdswDTQREk3LbzHoKOwNV0H/3tmyvIOvRl5HeYdJL0N7YhNSERvEtx6BE6ATutiGkPECfkJDcWHc81oKbEnpaNSdYbQTvNMpf4WvmeWWO6GdwnXHo33nJEyBkbAcnoEuxssgtbn/r2j5FJ9kdeT9AAn5HmZDZ7YaOvcc7MVbKsF0+9Y+q59dieZbJpqW/UFL7auntjY6xTRBybdTT7sdlaVtox5qQQfQ/YgvpMGCAkGBoEBQICgQFAgKBAWCAh2rwF+zttwFf+Tt/AAAAABJRU5ErkJggg==" width="36.5" height="18" style="width: 36.5px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="40" height="18" style="width: 40px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 40px; transform-origin: 489.078125px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; x = 3; A = 1;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    &gt;&gt; PS(A,x)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    ans =</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">        8.9683</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">Please present your answer rounded-off to nearest 4 decimal places.</span></span></div></div></div>

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Problem 57512. Easy Sequences 89: Double Summation of a Trigonometric Product

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