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受欢迎的三角函数 >

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

解答

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

解答

x = πn, x = \frac{3 π}{4} + πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: tan (x) = u

5 u + 5 u^{2} = 0

5 u + 5 u^{2} = 0 : u = 0, u = - 1

5 u + 5 u^{2} = 0

改写成标准形式

a x^{2} + b x + c = 0

5 u^{2} + 5 u = 0

使用求根公式求解

5 u^{2} + 5 u = 0

二次方程求根公式:

若

a = 5, b = 5, c = 0

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

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

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

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

使用法则

0 \cdot a = 0

= 5^{2} - 0

5^{2} - 0 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 5

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

将解分隔开

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

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

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

数字相加/相减:

- 5 + 5 = 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{- 5 - 5}{2 \cdot 5} : - 1

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

数字相减:

- 5 - 5 = - 10

= \frac{- 10}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{- 10}{10}

使用分式法则:

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

= - \frac{10}{10}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = 0, u = - 1

u = tan (x)

代回

tan (x) = 0, tan (x) = - 1

tan (x) = 0, tan (x) = - 1

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) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = - 1

tan (x) = - 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}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

合并所有解

x = πn, x = \frac{3 π}{4} + πn

作图

流行的例子

8sec^2(x)-8sec(x)=16

8 sec^{2} (x) - 8 sec (x) = 16

50=36sin((2pi)/(365)(t-101))+14

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14

sin(2θ-pi/3)=-1/2

sin (2 θ - \frac{π}{3}) = - \frac{1}{2}

7cos(θ)+sqrt(20)=0

7 cos (θ) + 20 = 0

sec^2(x)= 1/2 csc^2(x)+tan^2(x)

sec^{2} (x) = \frac{1}{2} csc^{2} (x) + tan^{2} (x)