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受欢迎的三角函数 >

4tan^2(x)=-sqrt(3)tan(x)+tan^2(x)

解答

4 tan^{2} (x) = - 3 tan (x) + tan^{2} (x)

解答

x = \frac{5 π}{6} + πn, x = πn

+1

度数

x = 15 0^{\circ} + 18 0^{\circ} n, x = 0^{\circ} + 18 0^{\circ} n

求解步骤

4 tan^{2} (x) = - 3 tan (x) + tan^{2} (x)

用替代法求解

4 tan^{2} (x) = - 3 tan (x) + tan^{2} (x)

令

: tan (x) = u

4 u^{2} = - 3 u + u^{2}

4 u^{2} = - 3 u + u^{2} : u = - \frac{3}{3}, u = 0

4 u^{2} = - 3 u + u^{2}

交换两边

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

将

4 u^{2}

para o lado esquerdo

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

两边减去

4 u^{2}

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

化简

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

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

改写成标准形式

a x^{2} + b x + c = 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 ( - 3 ) \cdot 0}{2 ( - 3 )}

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

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

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

使用法则

- (- a) = a

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

(- 3)^{2} = 3

(- 3)^{2}

使用指数法则:

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

若

n

是偶数

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

= (3)^{2}

使用根式运算法则:

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

= (3^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

分式相乘:

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

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

约分:

2

= 1

= 3

4 \cdot 3 \cdot 0 = 0

4 \cdot 3 \cdot 0

使用法则

0 \cdot a = 0

= 0

= 3 + 0

数字相加:

3 + 0 = 3

= 3

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

将解分隔开

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

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

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

去除括号:

(- a) = - a, - (- a) = a

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

同类项相加:

3 + 3 = 23

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

数字相乘:

2 \cdot 3 = 6

= \frac{2 3}{- 6}

使用分式法则:

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

= - \frac{2 3}{6}

约分:

2

= - \frac{3}{3}

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

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

去除括号:

(- a) = - a, - (- a) = a

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

同类项相加:

3 - 3 = 0

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

数字相乘:

2 \cdot 3 = 6

= \frac{0}{- 6}

使用分式法则:

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

= - \frac{0}{6}

使用法则

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

= - 0

= 0

二次方程组的解是:

u = - \frac{3}{3}, u = 0

u = tan (x)

代回

tan (x) = - \frac{3}{3}, tan (x) = 0

tan (x) = - \frac{3}{3}, tan (x) = 0

tan (x) = - \frac{3}{3} : x = \frac{5 π}{6} + πn

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

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

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 = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

tan (x) = 0 : x = πn

tan (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

合并所有解

x = \frac{5 π}{6} + πn, x = πn

作图

流行的例子

1/2 = 1/2*cos(4.2t+pi/6)

\frac{1}{2} = \frac{1}{2} \cdot cos (4.2 t + \frac{π}{6})

120=sqrt(83^2+75^2-2*83*75*cos(x))

120 = 8 3^{2} + 7 5^{2} - 2 \cdot 83 \cdot 75 \cdot cos (x)

cos (u) = \frac{7}{25}

sin(x)+cos(x)=1,0<= x<2pi

sin (x) + cos (x) = 1, 0 \leq x < 2 π

solvefor x,cos^2(x+y)=sin^2(x+y)

so l v e f or x, cos^{2} (x + y) = sin^{2} (x + y)