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受欢迎的三角函数 >

5tan^2(x)+3tan(x)=0

解答

5 tan^{2} (x) + 3 tan (x) = 0

解答

x = πn, x = - 0.54041 \dots + πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = - 30.96375 \dots^{\circ} + 18 0^{\circ} n

求解步骤

5 tan^{2} (x) + 3 tan (x) = 0

用替代法求解

5 tan^{2} (x) + 3 tan (x) = 0

令

: tan (x) = u

5 u^{2} + 3 u = 0

5 u^{2} + 3 u = 0 : u = 0, u = - \frac{3}{5}

5 u^{2} + 3 u = 0

使用求根公式求解

5 u^{2} + 3 u = 0

二次方程求根公式:

若

a = 5, b = 3, c = 0

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 5 \cdot 0}{2 \cdot 5}

u_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 5 \cdot 0}{2 \cdot 5}

3^{2} - 4 \cdot 5 \cdot 0 = 3

3^{2} - 4 \cdot 5 \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 5}

将解分隔开

u_{1} = \frac{- 3 + 3}{2 \cdot 5}, u_{2} = \frac{- 3 - 3}{2 \cdot 5}

u = \frac{- 3 + 3}{2 \cdot 5} : 0

\frac{- 3 + 3}{2 \cdot 5}

数字相加/相减:

- 3 + 3 = 0

= \frac{0}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{0}{10}

使用法则

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

= 0

u = \frac{- 3 - 3}{2 \cdot 5} : - \frac{3}{5}

\frac{- 3 - 3}{2 \cdot 5}

数字相减:

- 3 - 3 = - 6

= \frac{- 6}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{- 6}{10}

使用分式法则:

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

= - \frac{6}{10}

约分:

2

= - \frac{3}{5}

二次方程组的解是:

u = 0, u = - \frac{3}{5}

u = tan (x)

代回

tan (x) = 0, tan (x) = - \frac{3}{5}

tan (x) = 0, tan (x) = - \frac{3}{5}

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

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

tan (x) = - \frac{3}{5}

使用反三角函数性质

tan (x) = - \frac{3}{5}

tan (x) = - \frac{3}{5}

的通解

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

x = arctan (- \frac{3}{5}) + πn

x = arctan (- \frac{3}{5}) + πn

合并所有解

x = πn, x = arctan (- \frac{3}{5}) + πn

以小数形式表示解

x = πn, x = - 0.54041 \dots + πn

作图

流行的例子

sin(2x)+4=3sin(2x)-5

sin (2 x) + 4 = 3 sin (2 x) - 5

3 cos^{2} (x) - 1 = 0

-cos(2x)+cos(x)=0

- cos (2 x) + cos (x) = 0

solvefor x,cos(x)+sin(y)=1

so l v e f or x, cos (x) + sin (y) = 1

sin^2(x)+3sin(x)+1=0

sin^{2} (x) + 3 sin (x) + 1 = 0