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受欢迎的三角函数 >

1/(sin(x))-sin(x)=sin(x)

解答

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

解答

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: sin (x) = u

\frac{1}{u} - u = u

\frac{1}{u} - u = u : u = \frac{1}{2}, u = - \frac{1}{2}

\frac{1}{u} - u = u

在两边乘以

u

\frac{1}{u} - u = u

在两边乘以

u

\frac{1}{u} u - uu = uu

化简

\frac{1}{u} u - uu = uu

化简

\frac{1}{u} u : 1

\frac{1}{u} u

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot u}{u}

约分:

u

= 1

化简

- uu : - u^{2}

- uu

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

uu = u^{1 + 1}

= - u^{1 + 1}

数字相加:

1 + 1 = 2

= - u^{2}

化简

uu : u^{2}

uu

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

uu = u^{1 + 1}

= u^{1 + 1}

数字相加:

1 + 1 = 2

= u^{2}

1 - u^{2} = u^{2}

1 - u^{2} = u^{2}

1 - u^{2} = u^{2}

解

1 - u^{2} = u^{2} : u = \frac{1}{2}, u = - \frac{1}{2}

1 - u^{2} = u^{2}

将

1

到右边

1 - u^{2} = u^{2}

两边减去

1

1 - u^{2} - 1 = u^{2} - 1

化简

- u^{2} = u^{2} - 1

- u^{2} = u^{2} - 1

将

u^{2}

para o lado esquerdo

- u^{2} = u^{2} - 1

两边减去

u^{2}

- u^{2} - u^{2} = u^{2} - 1 - u^{2}

化简

- 2 u^{2} = - 1

- 2 u^{2} = - 1

两边除以

- 2

- 2 u^{2} = - 1

两边除以

- 2

\frac{- 2 u ^{2}}{- 2} = \frac{- 1}{- 2}

化简

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{1}{2}, u = - \frac{1}{2}

u = \frac{1}{2}, u = - \frac{1}{2}

验证解

找到无定义的点（奇点）:

u = 0

取

\frac{1}{u} - u

的分母，令其等于零

u = 0

以下点无定义

u = 0

将不在定义域的点与解相综合:

u = \frac{1}{2}, u = - \frac{1}{2}

u = sin (x)

代回

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

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

sin (x) = \frac{1}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

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

sin (x) = \frac{1}{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

sin (x) = - \frac{1}{2} : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

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

sin (x) = - \frac{1}{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{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

合并所有解

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

作图

流行的例子

4 cos^{2} (x) = 0

sin(2x)=(2*10*1500000)/(11000000)

sin (2 x) = \frac{2 \cdot 10 \cdot 1500000}{11000000}

2/(tan(x))=3-tan(x)

\frac{2}{tan ( x )} = 3 - tan (x)

tan (x) = 0.158

-1=sin(4.18879x)

- 1 = sin (4.18879 x)