解
arcsin(900x2+1900x2−1)=1.18
解
x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
解答ステップ
arcsin(900x2+1900x2−1)=1.18
三角関数の逆数プロパティを適用する
arcsin(900x2+1900x2−1)=1.18
arcsin(x)=a⇒x=sin(a)900x2+1900x2−1=sin(1.18)
sin(1.18)=sin(5059)
sin(1.18)
900x2+1900x2−1=sin(5059)
900x2+1900x2−1=sin(5059)
解く 900x2+1900x2−1=sin(5059):x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
900x2+1900x2−1=sin(5059)
以下で両辺を乗じる:900x2+1
900x2+1900x2−1=sin(5059)
以下で両辺を乗じる:900x2+1900x2+1900x2−1(900x2+1)=sin(5059)(900x2+1)
簡素化900x2−1=sin(5059)(900x2+1)
900x2−1=sin(5059)(900x2+1)
解く 900x2−1=sin(5059)(900x2+1):x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
900x2−1=sin(5059)(900x2+1)
1を右側に移動します
900x2−1=sin(5059)(900x2+1)
両辺に1を足す900x2−1+1=sin(5059)(900x2+1)+1
簡素化900x2=sin(5059)(900x2+1)+1
900x2=sin(5059)(900x2+1)+1
sin(5059)(900x2+1)を左側に移動します
900x2=sin(5059)(900x2+1)+1
両辺からsin(5059)(900x2+1)を引く900x2−sin(5059)(900x2+1)=sin(5059)(900x2+1)+1−sin(5059)(900x2+1)
簡素化900x2−sin(5059)(900x2+1)=1
900x2−sin(5059)(900x2+1)=1
拡張 −sin(5059)(900x2+1):−900sin(5059)x2−sin(5059)
−sin(5059)(900x2+1)
分配法則を適用する: a(b+c)=ab+aca=−sin(5059),b=900x2,c=1=−sin(5059)⋅900x2+(−sin(5059))⋅1
マイナス・プラスの規則を適用する+(−a)=−a=−900sin(5059)x2−1⋅sin(5059)
乗算:1⋅sin(5059)=sin(5059)=−900sin(5059)x2−sin(5059)
900x2−900sin(5059)x2−sin(5059)=1
sin(5059)を右側に移動します
900x2−900sin(5059)x2−sin(5059)=1
両辺にsin(5059)を足す900x2−900sin(5059)x2−sin(5059)+sin(5059)=1+sin(5059)
簡素化900x2−900sin(5059)x2=1+sin(5059)
900x2−900sin(5059)x2=1+sin(5059)
因数 900x2−900sin(5059)x2:900(1−sin(5059))x2
900x2−900sin(5059)x2
書き換え=1⋅900x2−900x2sin(5059)
共通項をくくり出す 900x2=900x2(1−sin(5059))
900(1−sin(5059))x2=1+sin(5059)
以下で両辺を割る900(1−sin(5059))
900(1−sin(5059))x2=1+sin(5059)
以下で両辺を割る900(1−sin(5059))900(1−sin(5059))900(1−sin(5059))x2=900(1−sin(5059))1+900(1−sin(5059))sin(5059)
簡素化
900(1−sin(5059))900(1−sin(5059))x2=900(1−sin(5059))1+900(1−sin(5059))sin(5059)
簡素化 900(1−sin(5059))900(1−sin(5059))x2:x2
900(1−sin(5059))900(1−sin(5059))x2
数を割る:900900=1=1−sin(5059)(−sin(5059)+1)x2
共通因数を約分する:1−sin(5059)=x2
簡素化 900(1−sin(5059))1+900(1−sin(5059))sin(5059):900(1−sin(5059))1+sin(5059)
900(1−sin(5059))1+900(1−sin(5059))sin(5059)
分母が等しいので, 分数を組み合わせる: ca±cb=ca±b=900(1−sin(5059))1+sin(5059)
x2=900(1−sin(5059))1+sin(5059)
x2=900(1−sin(5059))1+sin(5059)
x2=900(1−sin(5059))1+sin(5059)
x2=f(a) の場合, 解は x=f(a),−f(a)
x=900(1−sin(5059))1+sin(5059),x=−900(1−sin(5059))1+sin(5059)
900(1−sin(5059))1+sin(5059)=301−sin(5059)1+sin(5059)
900(1−sin(5059))1+sin(5059)
累乗根の規則を適用する:nba=nbna,, 以下を想定 a≥0,b≥0=900(−sin(5059)+1)1+sin(5059)
累乗根の規則を適用する:nab=nanb,, 以下を想定 a≥0,b≥0900(−sin(5059)+1)=900−sin(5059)+1=900−sin(5059)+11+sin(5059)
900=30
900
数を因数に分解する:900=302=302
累乗根の規則を適用する: nan=a302=30=30
=30−sin(5059)+11+sin(5059)
=301−sin(5059)1+sin(5059)
−900(1−sin(5059))1+sin(5059)=−301−sin(5059)1+sin(5059)
−900(1−sin(5059))1+sin(5059)
簡素化 900(1−sin(5059))1+sin(5059):30−sin(5059)+11+sin(5059)
900(1−sin(5059))1+sin(5059)
累乗根の規則を適用する:nba=nbna,, 以下を想定 a≥0,b≥0=900(−sin(5059)+1)1+sin(5059)
累乗根の規則を適用する:nab=nanb,, 以下を想定 a≥0,b≥0900(−sin(5059)+1)=900−sin(5059)+1=900−sin(5059)+11+sin(5059)
900=30
900
数を因数に分解する:900=302=302
累乗根の規則を適用する: nan=a302=30=30
=30−sin(5059)+11+sin(5059)
=−30−sin(5059)+1sin(5059)+1
=−301−sin(5059)1+sin(5059)
x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)