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受欢迎的三角函数 >

sin(x+20)*csc(70)=1

解答

sin (x + 2 0^{\circ}) \cdot csc (7 0^{\circ}) = 1

解答

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

+1

弧度

x = 1.22173 \dots - \frac{π}{9} + 2 πn, x = π - 1.22173 \dots - \frac{π}{9} + 2 πn

求解步骤

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

两边除以

csc (7 0^{\circ})

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

两边除以

csc (7 0^{\circ})

\frac{sin ( x + 2 0 ^{\circ} ) csc ( 7 0 ^{\circ} )}{csc ( 7 0 ^{\circ} )} = \frac{1}{csc ( 7 0 ^{\circ} )}

化简

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

使用反三角函数性质

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

解

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

将

2 0^{\circ}

到右边

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

两边减去

2 0^{\circ}

x + 2 0^{\circ} - 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

化简

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

解

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

将

2 0^{\circ}

到右边

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

两边减去

2 0^{\circ}

x + 2 0^{\circ} - 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

化简

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

以小数形式表示解

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

作图

流行的例子

solvefor x,t=tan(x/2)

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sin(x)+cos(x)=0,0<= x<= 360