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受欢迎的三角函数 >

tan^2(x)-3.31tan(x)+1.55=0

解答

tan^{2} (x) - 3.31 tan (x) + 1.55 = 0

解答

x = 1.22149 \dots + πn, x = 0.51396 \dots + πn

+1

度数

x = 69.98622 \dots^{\circ} + 18 0^{\circ} n, x = 29.44802 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) - 3.31 tan (x) + 1.55 = 0

用替代法求解

tan^{2} (x) - 3.31 tan (x) + 1.55 = 0

令

: tan (x) = u

u^{2} - 3.31 u + 1.55 = 0

u^{2} - 3.31 u + 1.55 = 0 : u = \frac{331 + 47561}{200}, u = \frac{331 - 47561}{200}

u^{2} - 3.31 u + 1.55 = 0

在两边乘以

100

u^{2} - 3.31 u + 1.55 = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

u^{2} \cdot 100 - 3.31 u \cdot 100 + 1.55 \cdot 100 = 0 \cdot 100

整理后得

100 u^{2} - 331 u + 155 = 0

100 u^{2} - 331 u + 155 = 0

使用求根公式求解

100 u^{2} - 331 u + 155 = 0

二次方程求根公式:

若

a = 100, b = - 331, c = 155

u_{1, 2} = \frac{- ( - 331 ) \pm ( - 331 ) ^{2} - 4 \cdot 100 \cdot 155}{2 \cdot 100}

u_{1, 2} = \frac{- ( - 331 ) \pm ( - 331 ) ^{2} - 4 \cdot 100 \cdot 155}{2 \cdot 100}

(- 331)^{2} - 4 \cdot 100 \cdot 155 = 47561

(- 331)^{2} - 4 \cdot 100 \cdot 155

使用指数法则:

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

若

n

是偶数

(- 331)^{2} = 33 1^{2}

= 33 1^{2} - 4 \cdot 100 \cdot 155

数字相乘:

4 \cdot 100 \cdot 155 = 62000

= 33 1^{2} - 62000

33 1^{2} = 109561

= 109561 - 62000

数字相减:

109561 - 62000 = 47561

= 47561

u_{1, 2} = \frac{- ( - 331 ) \pm 47561}{2 \cdot 100}

将解分隔开

u_{1} = \frac{- ( - 331 ) + 47561}{2 \cdot 100}, u_{2} = \frac{- ( - 331 ) - 47561}{2 \cdot 100}

u = \frac{- ( - 331 ) + 47561}{2 \cdot 100} : \frac{331 + 47561}{200}

\frac{- ( - 331 ) + 47561}{2 \cdot 100}

使用法则

- (- a) = a

= \frac{331 + 47561}{2 \cdot 100}

数字相乘:

2 \cdot 100 = 200

= \frac{331 + 47561}{200}

u = \frac{- ( - 331 ) - 47561}{2 \cdot 100} : \frac{331 - 47561}{200}

\frac{- ( - 331 ) - 47561}{2 \cdot 100}

使用法则

- (- a) = a

= \frac{331 - 47561}{2 \cdot 100}

数字相乘:

2 \cdot 100 = 200

= \frac{331 - 47561}{200}

二次方程组的解是:

u = \frac{331 + 47561}{200}, u = \frac{331 - 47561}{200}

u = tan (x)

代回

tan (x) = \frac{331 + 47561}{200}, tan (x) = \frac{331 - 47561}{200}

tan (x) = \frac{331 + 47561}{200}, tan (x) = \frac{331 - 47561}{200}

tan (x) = \frac{331 + 47561}{200} : x = arctan (\frac{331 + 47561}{200}) + πn

tan (x) = \frac{331 + 47561}{200}

使用反三角函数性质

tan (x) = \frac{331 + 47561}{200}

tan (x) = \frac{331 + 47561}{200}

的通解

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

x = arctan (\frac{331 + 47561}{200}) + πn

x = arctan (\frac{331 + 47561}{200}) + πn

tan (x) = \frac{331 - 47561}{200} : x = arctan (\frac{331 - 47561}{200}) + πn

tan (x) = \frac{331 - 47561}{200}

使用反三角函数性质

tan (x) = \frac{331 - 47561}{200}

tan (x) = \frac{331 - 47561}{200}

的通解

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

x = arctan (\frac{331 - 47561}{200}) + πn

x = arctan (\frac{331 - 47561}{200}) + πn

合并所有解

x = arctan (\frac{331 + 47561}{200}) + πn, x = arctan (\frac{331 - 47561}{200}) + πn

以小数形式表示解

x = 1.22149 \dots + πn, x = 0.51396 \dots + πn

作图

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