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受欢迎的三角函数 >

sqrt(3)tan^2(θ)+2tan(θ)-sqrt(3)=0

解答

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

解答

θ = \frac{π}{6} + πn, θ = \frac{2 π}{3} + πn

+1

度数

θ = 3 0^{\circ} + 18 0^{\circ} n, θ = 12 0^{\circ} + 18 0^{\circ} n

求解步骤

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

用替代法求解

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

令

: tan (θ) = u

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

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

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

使用求根公式求解

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

二次方程求根公式:

若

a = 3, b = 2, c = - 3

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

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

2^{2} - 43 (- 3) = 4

2^{2} - 43 (- 3)

使用法则

- (- a) = a

= 2^{2} + 433

433 = 12

433

使用根式运算法则:

a a = a

33 = 3

= 4 \cdot 3

数字相乘:

4 \cdot 3 = 12

= 12

= 2^{2} + 12

2^{2} = 4

= 4 + 12

数字相加:

4 + 12 = 16

= 16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

u_{1, 2} = \frac{- 2 \pm 4}{2 3}

将解分隔开

u_{1} = \frac{- 2 + 4}{2 3}, u_{2} = \frac{- 2 - 4}{2 3}

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

\frac{- 2 + 4}{2 3}

数字相加/相减:

- 2 + 4 = 2

= \frac{2}{2 3}

数字相除:

\frac{2}{2} = 1

= \frac{1}{3}

\frac{1}{3}

有理化:

\frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

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

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

u = \frac{- 2 - 4}{2 3} : - 3

\frac{- 2 - 4}{2 3}

数字相减:

- 2 - 4 = - 6

= \frac{- 6}{2 3}

使用分式法则:

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

= - \frac{6}{2 3}

数字相除:

\frac{6}{2} = 3

= \frac{3}{3}

使用根式运算法则:

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

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

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

使用指数法则:

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

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

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

数字相减:

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

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

使用根式运算法则:

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

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

= - 3

二次方程组的解是:

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

u = tan (θ)

代回

tan (θ) = \frac{3}{3}, tan (θ) = - 3

tan (θ) = \frac{3}{3}, tan (θ) = - 3

tan (θ) = \frac{3}{3} : θ = \frac{π}{6} + πn

tan (θ) = \frac{3}{3}

tan (θ) = \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}

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

tan (θ) = - 3 : θ = \frac{2 π}{3} + πn

tan (θ) = - 3

tan (θ) = - 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}

θ = \frac{2 π}{3} + πn

θ = \frac{2 π}{3} + πn

合并所有解

θ = \frac{π}{6} + πn, θ = \frac{2 π}{3} + πn

作图

流行的例子

sec (x) = \frac{25}{7}

sin(x/2)= 1/2 sin(x)

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

csc(2θ)= 1/2 (sec(θ))(cos(θ))

csc (2 θ) = \frac{1}{2} (sec (θ)) (cos (θ))

sec^2(x)+2sec(x)-8=0

sec^{2} (x) + 2 sec (x) - 8 = 0

3cos^2(x)+4sin(x)-4=0

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