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受欢迎的三角函数 >

solvefor c,e=r(sec(c/2)-1)

解答

求解

c, e = r (sec (\frac{c}{2}) - 1)

解答

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

求解步骤

e = r (sec (\frac{c}{2}) - 1)

交换两边

r (sec (\frac{c}{2}) - 1) = e

两边除以

r; r \neq = 0

r (sec (\frac{c}{2}) - 1) = e

两边除以

r; r \neq = 0

\frac{r ( sec ( \frac{c}{2} ) - 1 )}{r} = \frac{e}{r}; r \neq = 0

化简

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

将

1

到右边

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

两边加上

1

sec (\frac{c}{2}) - 1 + 1 = \frac{e}{r} + 1; r \neq = 0

化简

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

使用反三角函数性质

sec (\frac{c}{2}) = \frac{e}{r} + 1

sec (\frac{c}{2}) = \frac{e}{r} + 1

的通解

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

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

解

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn : c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

在两边乘以

2

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

在两边乘以

2

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

化简

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

化简

\frac{2 c}{2} : c

\frac{2 c}{2}

数字相除:

\frac{2}{2} = 1

= c

化简

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : 2 arcsec (\frac{e}{r} + 1) + 4 πn

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

解

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn : c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

在两边乘以

2

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

在两边乘以

2

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

化简

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

化简

\frac{2 c}{2} : c

\frac{2 c}{2}

数字相除:

\frac{2}{2} = 1

= c

化简

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : - 2 arcsec (\frac{e}{r} + 1) + 4 πn

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

作图

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