[{"data":1,"prerenderedAt":169},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Ftrigonometric-composition":3},{"topic":4,"category":135,"seo":139,"breadcrumbs":144,"prerequisites":151,"nextTopics":161,"relatedTopics":168},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":21,"learningGoal":25,"blocks":26},"high-school-mathematics-ii-trigonometric-functions-trigonometric-composition","trigonometric-composition","三角関数の合成","a sin x+b cos xを一つの正弦関数へ合成し、係数の直角三角形から振幅と位相を求めます。","\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Ftrigonometric-composition","\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions","beginner","student_high",6,"2026-07-27","ai_generated",[17,18,19,20],"数学II","三角関数","合成","振幅",[22,23,24],"加法定理","三角関数の相互関係","正弦波の変換","a sin x+b cos xを一つの正弦関数へ合成し、振幅と位相を係数と図から求められるようになる。",[27,32,41,62,68,78,88,94,100,116,125],{"id":28,"type":29,"title":7,"subtitle":30,"shortDefinition":31},"hero","HeroBlock","二つの係数を振幅と位相へまとめる","同じ角xをもつsinとcosの和は、形が異なる二つの波ではなく、位相がずれた一つの正弦波として表せます。係数a,bを直角三角形の辺として読みます。",{"id":33,"type":34,"term":7,"definition":35,"plainExplanation":36,"keywords":37},"definition","DefinitionBlock","a sin x+b cos xをR sin(x+φ)など一つの三角関数へ書き換えることです。","加法定理でR 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sin(x+φ)","Rcosφ=a、Rsinφ=bとなるRとφを選ぶ。",[51,54,57],{"symbol":52,"meaning":53},"a,b","元のsin項とcos項の係数",{"symbol":55,"meaning":56},"R","合成後の振幅√(a²+b²)",{"symbol":58,"meaning":59},"φ","係数の符号も満たす位相","sinの係数がRcosφ、cosの係数がRsinφ","最初にRを三平方で求め、次にcosφ=a\u002FR、sinφ=b\u002FRから象限を含めてφを決めます。",{"id":63,"type":64,"src":65,"alt":66,"caption":67},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Ftrigonometric-composition\u002Ftrigonometric-composition.svg","係数aとbを直角三角形の二辺、Rを斜辺、φを角として合成の係数対応を示す図","横辺a、縦辺b、斜辺R=√(a²+b²)の直角三角形を描き、cosφ=a\u002FR、sinφ=b\u002FRを示します。右側で加法定理の係数と一対一に結びます。",{"id":69,"type":70,"steps":71,"title":77},"steps","StepBlock",[72,73,74,75,76],"sin xの係数aとcos xの係数bを読む","R=√(a²+b²)を求める","cosφ=a\u002FR、sinφ=b\u002FRを置く","a,bの符号からφの象限を決める","R 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