解答
arcsin(900x2+1900x2−1)=1.18
解答
x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
求解步骤
arcsin(900x2+1900x2−1)=1.18
使用反三角函数性质
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 900x2+1900x2−1=sin(5059):x=301−sin(5059)1+sin(5059),x=−301−sin(5059)1+sin(5059)
900x2+1900x2−1=sin(5059)
在两边乘以 900x2+1
900x2+1900x2−1=sin(5059)
在两边乘以 900x2+1900x2+1900x2−1(900x2+1)=sin(5059)(900x2+1)
化简900x2−1=sin(5059)(900x2+1)
900x2−1=sin(5059)(900x2+1)
解 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)
将 1到右边
900x2−1=sin(5059)(900x2+1)
两边加上 1900x2−1+1=sin(5059)(900x2+1)+1
化简900x2=sin(5059)(900x2+1)+1
900x2=sin(5059)(900x2+1)+1
将 sin(5059)(900x2+1)para o lado esquerdo
900x2=sin(5059)(900x2+1)+1
两边减去 sin(5059)(900x2+1)900x2−sin(5059)(900x2+1)=sin(5059)(900x2+1)+1−sin(5059)(900x2+1)
化简900x2−sin(5059)(900x2+1)=1
900x2−sin(5059)(900x2+1)=1
乘开 −sin(5059)(900x2+1):−900sin(5059)x2−sin(5059)
−sin(5059)(900x2+1)
使用分配律: a(b+c)=ab+aca=−sin(5059),b=900x2,c=1=−sin(5059)⋅900x2+(−sin(5059))⋅1
使用加减运算法则+(−a)=−a=−900sin(5059)x2−1⋅sin(5059)
乘以:1⋅sin(5059)=sin(5059)=−900sin(5059)x2−sin(5059)
900x2−900sin(5059)x2−sin(5059)=1
将 sin(5059)到右边
900x2−900sin(5059)x2−sin(5059)=1
两边加上 sin(5059)900x2−900sin(5059)x2−sin(5059)+sin(5059)=1+sin(5059)
化简900x2−900sin(5059)x2=1+sin(5059)
900x2−900sin(5059)x2=1+sin(5059)
分解 900x2−900sin(5059)x2:900(1−sin(5059))x2
900x2−900sin(5059)x2
改写为=1⋅900x2−900x2sin(5059)
因式分解出通项 900x2=900x2(1−sin(5059))
900(1−sin(5059))x2=1+sin(5059)
两边除以 900(1−sin(5059))
900(1−sin(5059))x2=1+sin(5059)
两边除以 900(1−sin(5059))900(1−sin(5059))900(1−sin(5059))x2=900(1−sin(5059))1+900(1−sin(5059))sin(5059)
化简
900(1−sin(5059))900(1−sin(5059))x2=900(1−sin(5059))1+900(1−sin(5059))sin(5059)
化简 900(1−sin(5059))900(1−sin(5059))x2:x2
900(1−sin(5059))900(1−sin(5059))x2
数字相除:900900=1=1−sin(5059)(−sin(5059)+1)x2
约分:1−sin(5059)=x2
化简 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)
因为分母相等，所以合并分式: 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)
对于 x2=f(a) 解为 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)
使用根式运算法则: 假定 a≥0,b≥0=900(−sin(5059)+1)1+sin(5059)
使用根式运算法则: 假定 a≥0,b≥0900(−sin(5059)+1)=900−sin(5059)+1=900−sin(5059)+11+sin(5059)
900=30
900
因式分解数字: 900=302=302
使用根式运算法则: 302=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)
化简 900(1−sin(5059))1+sin(5059):30−sin(5059)+11+sin(5059)
900(1−sin(5059))1+sin(5059)
使用根式运算法则: 假定 a≥0,b≥0=900(−sin(5059)+1)1+sin(5059)
使用根式运算法则: 假定 a≥0,b≥0900(−sin(5059)+1)=900−sin(5059)+1=900−sin(5059)+11+sin(5059)
900=30
900
因式分解数字: 900=302=302
使用根式运算法则: 302=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)