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受欢迎的三角函数 >

3tan^2(α)-3tan(α)=0

解答

3 tan^{2} (α) - 3 tan (α) = 0

解答

α = \frac{π}{4} + πn, α = πn

+1

度数

α = 4 5^{\circ} + 18 0^{\circ} n, α = 0^{\circ} + 18 0^{\circ} n

求解步骤

3 tan^{2} (α) - 3 tan (α) = 0

用替代法求解

3 tan^{2} (α) - 3 tan (α) = 0

令

: tan (α) = u

3 u^{2} - 3 u = 0

3 u^{2} - 3 u = 0 : u = 1, u = 0

3 u^{2} - 3 u = 0

使用求根公式求解

3 u^{2} - 3 u = 0

二次方程求根公式:

若

a = 3, b = - 3, c = 0

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 3)^{2} - 4 \cdot 3 \cdot 0 = 3

(- 3)^{2} - 4 \cdot 3 \cdot 0

使用指数法则:

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

若

n

是偶数

(- 3)^{2} = 3^{2}

= 3^{2} - 4 \cdot 3 \cdot 0

使用法则

0 \cdot a = 0

= 3^{2} - 0

3^{2} - 0 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 3

u_{1, 2} = \frac{- ( - 3 ) \pm 3}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- ( - 3 ) + 3}{2 \cdot 3}, u_{2} = \frac{- ( - 3 ) - 3}{2 \cdot 3}

u = \frac{- ( - 3 ) + 3}{2 \cdot 3} : 1

\frac{- ( - 3 ) + 3}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{3 + 3}{2 \cdot 3}

数字相加:

3 + 3 = 6

= \frac{6}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{6}{6}

使用法则

\frac{a}{a} = 1

= 1

u = \frac{- ( - 3 ) - 3}{2 \cdot 3} : 0

\frac{- ( - 3 ) - 3}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{3 - 3}{2 \cdot 3}

数字相减:

3 - 3 = 0

= \frac{0}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{0}{6}

使用法则

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

= 0

二次方程组的解是:

u = 1, u = 0

u = tan (α)

代回

tan (α) = 1, tan (α) = 0

tan (α) = 1, tan (α) = 0

tan (α) = 1 : α = \frac{π}{4} + πn

tan (α) = 1

tan (α) = 1

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}

α = \frac{π}{4} + πn

α = \frac{π}{4} + πn

tan (α) = 0 : α = πn

tan (α) = 0

tan (α) = 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}

α = 0 + πn

α = 0 + πn

解

α = 0 + πn : α = πn

α = 0 + πn

0 + πn = πn

α = πn

α = πn

合并所有解

α = \frac{π}{4} + πn, α = πn

作图

流行的例子

cos (θ) = - \frac{12}{13}

- tan (x) = 0

3 sin (θ) + 1 = 1

csc^2(x)-3csc(x)-4=0

csc^{2} (x) - 3 csc (x) - 4 = 0

3 cos (x) = 2