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受欢迎的三角函数 >

1/(sin(x))=sqrt(2)

解答

\frac{1}{sin ( x )} = 2

解答

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

求解步骤

\frac{1}{sin ( x )} = 2

在两边乘以

sin (x)

\frac{1}{sin ( x )} = 2

在两边乘以

sin (x)

\frac{1}{sin ( x )} sin (x) = 2 sin (x)

化简

1 = 2 sin (x)

1 = 2 sin (x)

交换两边

2 sin (x) = 1

两边除以

2

2 sin (x) = 1

两边除以

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

化简

\frac{2 sin ( x )}{2} = \frac{1}{2}

化简

\frac{2 sin ( x )}{2} : sin (x)

\frac{2 sin ( x )}{2}

约分:

2

= sin (x)

化简

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

乘以共轭根式

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= \frac{2}{2}

sin (x) = \frac{2}{2}

sin (x) = \frac{2}{2}

sin (x) = \frac{2}{2}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{1}{sin ( x )}

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

sin (x) = \frac{2}{2}

sin (x) = \frac{2}{2}

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

作图

流行的例子

0 = sec (\frac{π x}{4})

3cos^2(x)+2cos(x)-1=0

3 cos^{2} (x) + 2 cos (x) - 1 = 0

arctan (θ) = - 2

sin(3x)-sin(x)=sin(3x-x)

sin (3 x) - sin (x) = sin (3 x - x)

sin(a)=-(sqrt(3))/2

sin (a) = - \frac{3}{2}