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受欢迎的三角函数 >

-sin^2(x)=sin^4(x)

解答

- sin^{2} (x) = sin^{4} (x)

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

- sin^{2} (x) = sin^{4} (x)

用替代法求解

- sin^{2} (x) = sin^{4} (x)

令

: sin (x) = u

- u^{2} = u^{4}

- u^{2} = u^{4} : u = 0, u = i, u = - i

- u^{2} = u^{4}

交换两边

u^{4} = - u^{2}

将

u^{2}

para o lado esquerdo

u^{4} = - u^{2}

两边加上

u^{2}

u^{4} + u^{2} = - u^{2} + u^{2}

化简

u^{4} + u^{2} = 0

u^{4} + u^{2} = 0

用

v = u^{2}

和

v^{2} = u^{4}

改写方程式

v^{2} + v = 0

解

v^{2} + v = 0 : v = 0, v = - 1

v^{2} + v = 0

使用求根公式求解

v^{2} + v = 0

二次方程求根公式:

若

a = 1, b = 1, c = 0

v_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

v_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot 0 = 1

1^{2} - 4 \cdot 1 \cdot 0

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 1 \cdot 0

使用法则

0 \cdot a = 0

= 1 - 0

数字相减:

1 - 0 = 1

= 1

使用法则

1 = 1

= 1

v_{1, 2} = \frac{- 1 \pm 1}{2 \cdot 1}

将解分隔开

v_{1} = \frac{- 1 + 1}{2 \cdot 1}, v_{2} = \frac{- 1 - 1}{2 \cdot 1}

v = \frac{- 1 + 1}{2 \cdot 1} : 0

\frac{- 1 + 1}{2 \cdot 1}

数字相加/相减:

- 1 + 1 = 0

= \frac{0}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{0}{2}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

v = \frac{- 1 - 1}{2 \cdot 1} : - 1

\frac{- 1 - 1}{2 \cdot 1}

数字相减:

- 1 - 1 = - 2

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 2}{2}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{2}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

v = 0, v = - 1

v = 0, v = - 1

代回

v = u^{2}

，求解

u

解

u^{2} = 0 : u = 0

u^{2} = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

u = 0

解

u^{2} = - 1 : u = i, u = - i

u^{2} = - 1

对于

x^{2} = f (a)

解为

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

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

解为

u = 0, u = i, u = - i

u = sin (x)

代回

sin (x) = 0, sin (x) = i, sin (x) = - i

sin (x) = 0, sin (x) = i, sin (x) = - i

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sin (x) = i :

无解

sin (x) = i

无解

sin (x) = - i :

无解

sin (x) = - i

无解

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

3cos^2(x)=sin(2x)*sin(x)

3 cos^{2} (x) = sin (2 x) \cdot sin (x)

csc (t) = 2

arccosh(θ)=0.86806

arccosh (θ) = 0.86806

sin (t) = \frac{5}{13}

sin(x)=-(sqrt(7))/4

sin (x) = - \frac{7}{4}