zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

tan^2(x)-9tan(x)-10=0

解答

tan^{2} (x) - 9 tan (x) - 10 = 0

解答

x = 1.47112 \dots + πn, x = \frac{3 π}{4} + πn

+1

度数

x = 84.28940 \dots^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) - 9 tan (x) - 10 = 0

用替代法求解

tan^{2} (x) - 9 tan (x) - 10 = 0

令

: tan (x) = u

u^{2} - 9 u - 10 = 0

u^{2} - 9 u - 10 = 0 : u = 10, u = - 1

u^{2} - 9 u - 10 = 0

使用求根公式求解

u^{2} - 9 u - 10 = 0

二次方程求根公式:

若

a = 1, b = - 9, c = - 10

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 1 \cdot ( - 10 )}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 1 \cdot ( - 10 )}{2 \cdot 1}

(- 9)^{2} - 4 \cdot 1 \cdot (- 10) = 11

(- 9)^{2} - 4 \cdot 1 \cdot (- 10)

使用法则

- (- a) = a

= (- 9)^{2} + 4 \cdot 1 \cdot 10

使用指数法则:

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

若

n

是偶数

(- 9)^{2} = 9^{2}

= 9^{2} + 4 \cdot 1 \cdot 10

数字相乘:

4 \cdot 1 \cdot 10 = 40

= 9^{2} + 40

9^{2} = 81

= 81 + 40

数字相加:

81 + 40 = 121

= 121

因式分解数字:

121 = 1 1^{2}

= 1 1^{2}

使用根式运算法则:

n a^{n} = a

1 1^{2} = 11

= 11

u_{1, 2} = \frac{- ( - 9 ) \pm 11}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- ( - 9 ) + 11}{2 \cdot 1}, u_{2} = \frac{- ( - 9 ) - 11}{2 \cdot 1}

u = \frac{- ( - 9 ) + 11}{2 \cdot 1} : 10

\frac{- ( - 9 ) + 11}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{9 + 11}{2 \cdot 1}

数字相加:

9 + 11 = 20

= \frac{20}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{20}{2}

数字相除:

\frac{20}{2} = 10

= 10

u = \frac{- ( - 9 ) - 11}{2 \cdot 1} : - 1

\frac{- ( - 9 ) - 11}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{9 - 11}{2 \cdot 1}

数字相减:

9 - 11 = - 2

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 2}{2}

使用分式法则:

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

= - \frac{2}{2}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

u = 10, u = - 1

u = tan (x)

代回

tan (x) = 10, tan (x) = - 1

tan (x) = 10, tan (x) = - 1

tan (x) = 10 : x = arctan (10) + πn

tan (x) = 10

使用反三角函数性质

tan (x) = 10

tan (x) = 10

的通解

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

x = arctan (10) + πn

x = arctan (10) + 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 = arctan (10) + πn, x = \frac{3 π}{4} + πn

以小数形式表示解

x = 1.47112 \dots + πn, x = \frac{3 π}{4} + πn

作图

流行的例子

(cot(θ)-1)(csc(θ)-1)=0

(cot (θ) - 1) (csc (θ) - 1) = 0

(tan(θ)-1)(sec(θ)+1)=0

(tan (θ) - 1) (sec (θ) + 1) = 0

9cos(x)-9sin(x)=0

9 cos (x) - 9 sin (x) = 0

sin^2(3x)-sin^2(x)=0

sin^{2} (3 x) - sin^{2} (x) = 0

sec^2(x)+6tan(x)+4=0

sec^{2} (x) + 6 tan (x) + 4 = 0