[{"data":1,"prerenderedAt":158},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Fgeneral-angles-and-terminal-sides":3},{"topic":4,"category":133,"seo":137,"breadcrumbs":142,"prerequisites":149,"nextTopics":150,"relatedTopics":157},{"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-general-angles-and-terminal-sides","general-angles-and-terminal-sides","一般角と動径","角を回転量として捉え、正負や1周を超える一般角の終辺と、同じ終辺をもつ角を正確に表します。","\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Fgeneral-angles-and-terminal-sides","\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions","beginner","student_high",5,"2026-07-27","ai_generated",[17,18,19,20],"数学II","三角関数","一般角","動径",[22,23,24],"三角比","円と角","正負の数","角を回転量として捉え、正負や1周を超える一般角の終辺と同じ終辺をもつ角を表せるようになる。",[27,32,42,60,66,76,86,92,98,114,123],{"id":28,"type":29,"title":7,"subtitle":30,"shortDefinition":31},"hero","HeroBlock","角を図形の大きさから回転量へ","三角関数では角を0°から180°までに限らず、何周でも回れる向き付きの量として扱います。同じ方向へ着く複数の角を一つの終辺で整理できます。",{"id":33,"type":34,"term":19,"definition":35,"plainExplanation":36,"keywords":37},"definition","DefinitionBlock","固定した始辺から動径を回転させた量で、正負や1周を超える値を含む角です。","反時計回りを正、時計回りを負とします。回転後の動径を終辺といい、360°の整数倍だけ違う角は同じ終辺をもちます。角の値は違っても三角関数の値が同じになる周期性の入口です。",[38,39,40,41],"始辺","終辺","正の回転","負の回転",{"id":43,"type":44,"title":45,"formulas":46,"strategy":59},"formula","FormulaBlock","同じ終辺をもつ角",[47],{"label":48,"expression":49,"meaning":50,"symbols":51,"tip":58},"一般形","θ+360°k  (kは整数)","角θに何周分かを加減した、同じ終辺をもつすべての角。",[52,55],{"symbol":53,"meaning":54},"θ","基準にする一つの角",{"symbol":56,"meaning":57},"k","正・0・負を含む周回数","基準範囲へ戻すときは360°を繰り返し加減する","回転方向を確認し、360°の整数倍を加減して終辺の位置を保ちます。",{"id":61,"type":62,"src":63,"alt":64,"caption":65},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Fgeneral-angles-and-terminal-sides\u002Fgeneral-angles-and-terminal-sides.svg","330度、マイナス30度、690度が同じ終辺に到達する回転を示す円の図","原点を共通中心とする長い実線弧330°、短い破線弧−30°に加え、外側の点線1周を「+360°」として示し、690°も同じ終辺へ到達することを表します。",{"id":67,"type":68,"steps":69,"title":75},"steps","StepBlock",[70,71,72,73,74],"始辺を正のx軸に置く","角の符号から回転方向を決める","360°を何回分含むかを取り除く","残った角で終辺の象限を決める","同じ終辺の角は360°kを付けて表す","終辺を判断する手順",{"id":77,"type":78,"title":79,"points":80,"body":85},"key-points","KeyPointBlock","角の値と終辺を区別する",[81,82,83,84],"1周は360°","正は反時計回り、負は時計回り","同じ終辺でも角の値は一つではない","象限は終辺の位置で決まる","330°、−30°、690°は回転の仕方や量が異なりますが、最終的な終辺は同じです。問題が角そのものを問うのか、終辺の方向や三角関数値を問うのかを分けます。同じ終辺をもつ角はθ+360°×k（kは整数）と表せるので、正の角一つだけで終えないようにします。",{"id":87,"type":88,"scenario":89,"explanation":90,"result":91},"example","ExampleBlock","角−30°と同じ終辺をもち、0°以上360°未満の角を求める。","−30°は時計回りに30°回した角です。360°を1周分加えると−30°+360°=330°です。回転量は変わりますが、1周加えただけなので終辺は同じです。","求める角は330°。同じ終辺をもつすべての角は−30°+360°kです。",{"id":93,"type":94,"warningTitle":95,"message":96,"severity":93,"action":97},"warning","WarningBlock","負の角を大きさのない角と思わない","負号は角が存在しない意味ではなく、標準の向きと反対の時計回りに回転することを表します。","数直線の負号ではなく、円上の回転矢印として描き、始辺から時計回りに進む向きを確認しましょう。",{"id":99,"type":100,"title":101,"questions":102},"quiz","QuizBlock","確認テスト",[103],{"question":104,"choices":105,"answerIndex":109,"choiceExplanations":110},"角690°と同じ終辺をもち、0°以上360°未満にある角はどれですか。",[106,107,108],"330°","30°","−330°",0,[111,112,113],"正解です。690°−360°=330°で、1周分だけ減らしても終辺は同じです。","690°から360°を引いた値は330°です。30°では終辺が第1象限になります。","範囲が0°以上なので負の角は条件を満たしません。",{"id":115,"type":116,"title":117,"points":118},"summary","SummaryBlock","まとめ",[119,120,121,122],"一般角は正負と何周分もの回転を含む","反時計回りが正、時計回りが負","360°の整数倍だけ違う角は同じ終辺","角の値と最終的な終辺を分けて考える",{"id":124,"type":125,"title":126,"nextTopics":127,"relatedKeywords":129},"next-action","NextActionBlock","角を弧の長さで測る",[128],"high-school-mathematics-ii-trigonometric-functions-radians-arcs-and-sectors",[130,131,132],"弧度法","ラジアン","扇形",{"path":10,"title":18,"description":134,"parentPath":135,"accentToken":136},"一般角、弧度法、三角関数のグラフ、相互関係、加法定理を整理していくカテゴリです。","\u002Fhigh-school\u002Fmathematics-ii","signal-blue",{"title":138,"description":139,"canonicalUrl":140,"ogImage":141},"一般角と動径 | 数学II 三角関数","始辺、終辺、回転方向、1周を超える角と負の角を一般角として整理します。","https:\u002F\u002Fzeqnilo.com\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Fgeneral-angles-and-terminal-sides","https:\u002F\u002Fzeqnilo.com\u002Fassets\u002Fsite\u002Fdefault-og.svg",[143,146,147,148],{"title":144,"path":145},"高校","\u002Fhigh-school",{"title":17,"path":135},{"title":18,"path":10},{"title":7,"path":9},[],[151],{"id":128,"title":152,"summary":153,"canonicalPath":154,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":155,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":156},"弧度法と扇形","弧度法を半径に対する弧長の比として理解し、度数法との変換と扇形の弧長・面積を一つの関係で求めます。","\u002Fhigh-school\u002Fmathematics-ii\u002Ftrigonometric-functions\u002Fradians-arcs-and-sectors",6,[17,18,130,132],[],1785565324610]