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受欢迎的三角函数 >

(4sec^2(x))/2 =-8sec(x)

解答

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

解答

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

+1

度数

x = 104.47751 \dots^{\circ} + 36 0^{\circ} n, x = - 104.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

用替代法求解

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

令

: sec (x) = u

\frac{4 u ^{2}}{2} = - 8 u

\frac{4 u ^{2}}{2} = - 8 u : u = 0, u = - 4

\frac{4 u ^{2}}{2} = - 8 u

在两边乘以

2

\frac{4 u ^{2}}{2} = - 8 u

在两边乘以

2

\frac{4 u ^{2}}{2} \cdot 2 = - 8 u \cdot 2

化简

4 u^{2} = - 16 u

4 u^{2} = - 16 u

将

16 u

para o lado esquerdo

4 u^{2} = - 16 u

两边加上

16 u

4 u^{2} + 16 u = - 16 u + 16 u

化简

4 u^{2} + 16 u = 0

4 u^{2} + 16 u = 0

使用求根公式求解

4 u^{2} + 16 u = 0

二次方程求根公式:

若

a = 4, b = 16, c = 0

u_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 4 \cdot 0}{2 \cdot 4}

u_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 4 \cdot 0}{2 \cdot 4}

1 6^{2} - 4 \cdot 4 \cdot 0 = 16

1 6^{2} - 4 \cdot 4 \cdot 0

使用法则

0 \cdot a = 0

= 1 6^{2} - 0

1 6^{2} - 0 = 1 6^{2}

= 1 6^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 16

u_{1, 2} = \frac{- 16 \pm 16}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- 16 + 16}{2 \cdot 4}, u_{2} = \frac{- 16 - 16}{2 \cdot 4}

u = \frac{- 16 + 16}{2 \cdot 4} : 0

\frac{- 16 + 16}{2 \cdot 4}

数字相加/相减:

- 16 + 16 = 0

= \frac{0}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{0}{8}

使用法则

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

= 0

u = \frac{- 16 - 16}{2 \cdot 4} : - 4

\frac{- 16 - 16}{2 \cdot 4}

数字相减:

- 16 - 16 = - 32

= \frac{- 32}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{- 32}{8}

使用分式法则:

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

= - \frac{32}{8}

数字相除:

\frac{32}{8} = 4

= - 4

二次方程组的解是:

u = 0, u = - 4

u = sec (x)

代回

sec (x) = 0, sec (x) = - 4

sec (x) = 0, sec (x) = - 4

sec (x) = 0 :

无解

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

无解

sec (x) = - 4 : x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

sec (x) = - 4

使用反三角函数性质

sec (x) = - 4

sec (x) = - 4

的通解

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

合并所有解

x = arcsec (- 4) + 2 πn, x = - arcsec (- 4) + 2 πn

以小数形式表示解

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

作图

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