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受欢迎的三角函数 >

6sec(2x)-8=0

解答

6 sec (2 x) - 8 = 0

解答

x = \frac{0.72273 \dots}{2} + πn, x = π - \frac{0.72273 \dots}{2} + πn

+1

度数

x = 20.70481 \dots^{\circ} + 18 0^{\circ} n, x = 159.29518 \dots^{\circ} + 18 0^{\circ} n

求解步骤

6 sec (2 x) - 8 = 0

将

8

到右边

6 sec (2 x) - 8 = 0

两边加上

8

6 sec (2 x) - 8 + 8 = 0 + 8

化简

6 sec (2 x) = 8

6 sec (2 x) = 8

两边除以

6

6 sec (2 x) = 8

两边除以

6

\frac{6 sec ( 2 x )}{6} = \frac{8}{6}

化简

sec (2 x) = \frac{4}{3}

sec (2 x) = \frac{4}{3}

使用反三角函数性质

sec (2 x) = \frac{4}{3}

sec (2 x) = \frac{4}{3}

的通解

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

2 x = arcsec (\frac{4}{3}) + 2 πn, 2 x = 2 π - arcsec (\frac{4}{3}) + 2 πn

2 x = arcsec (\frac{4}{3}) + 2 πn, 2 x = 2 π - arcsec (\frac{4}{3}) + 2 πn

解

2 x = arcsec (\frac{4}{3}) + 2 πn : x = \frac{arcsec ( \frac{4}{3} )}{2} + πn

2 x = arcsec (\frac{4}{3}) + 2 πn

两边除以

2

2 x = arcsec (\frac{4}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arcsec ( \frac{4}{3} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arcsec ( \frac{4}{3} )}{2} + πn

x = \frac{arcsec ( \frac{4}{3} )}{2} + πn

解

2 x = 2 π - arcsec (\frac{4}{3}) + 2 πn : x = π - \frac{arcsec ( \frac{4}{3} )}{2} + πn

2 x = 2 π - arcsec (\frac{4}{3}) + 2 πn

两边除以

2

2 x = 2 π - arcsec (\frac{4}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arcsec ( \frac{4}{3} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arcsec ( \frac{4}{3} )}{2} + πn

x = π - \frac{arcsec ( \frac{4}{3} )}{2} + πn

x = \frac{arcsec ( \frac{4}{3} )}{2} + πn, x = π - \frac{arcsec ( \frac{4}{3} )}{2} + πn

以小数形式表示解

x = \frac{0.72273 \dots}{2} + πn, x = π - \frac{0.72273 \dots}{2} + πn

作图

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