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受欢迎的三角函数 >

6tan(x)=tan^2(x),x=0

解答

6 tan (x) = tan^{2} (x), x = 0

解答

x = 0

+1

度数

x = 0^{\circ}

求解步骤

6 tan (x) = tan^{2} (x), x = 0

用替代法求解

6 tan (x) = tan^{2} (x)

令

: tan (x) = u

6 u = u^{2}

6 u = u^{2} : u = 6, u = 0

6 u = u^{2}

交换两边

u^{2} = 6 u

将

6 u

para o lado esquerdo

u^{2} = 6 u

两边减去

6 u

u^{2} - 6 u = 6 u - 6 u

化简

u^{2} - 6 u = 0

u^{2} - 6 u = 0

使用求根公式求解

u^{2} - 6 u = 0

二次方程求根公式:

若

a = 1, b = - 6, c = 0

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot 0 = 6

(- 6)^{2} - 4 \cdot 1 \cdot 0

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 6)^{2} = 6^{2}

= 6^{2} - 4 \cdot 1 \cdot 0

使用法则

0 \cdot a = 0

= 6^{2} - 0

6^{2} - 0 = 6^{2}

= 6^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 6

u_{1, 2} = \frac{- ( - 6 ) \pm 6}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- ( - 6 ) + 6}{2 \cdot 1}, u_{2} = \frac{- ( - 6 ) - 6}{2 \cdot 1}

u = \frac{- ( - 6 ) + 6}{2 \cdot 1} : 6

\frac{- ( - 6 ) + 6}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{6 + 6}{2 \cdot 1}

数字相加:

6 + 6 = 12

= \frac{12}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{12}{2}

数字相除:

\frac{12}{2} = 6

= 6

u = \frac{- ( - 6 ) - 6}{2 \cdot 1} : 0

\frac{- ( - 6 ) - 6}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{6 - 6}{2 \cdot 1}

数字相减:

6 - 6 = 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

二次方程组的解是:

u = 6, u = 0

u = tan (x)

代回

tan (x) = 6, tan (x) = 0

tan (x) = 6, tan (x) = 0

tan (x) = 6, x = 0 :

无解

tan (x) = 6, x = 0

使用反三角函数性质

tan (x) = 6

tan (x) = 6

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (6) + πn

x = arctan (6) + πn

在

x = 0

范围内的解

无解

tan (x) = 0, x = 0 : x = 0

tan (x) = 0, x = 0

tan (x) = 0

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

在

x = 0

范围内的解

x = 0

合并所有解

x = 0

作图

流行的例子

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so l v e f or a, sin (arccos (x)) = 1 - x^{2}

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