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受欢迎的三角函数 >

sec(θ/5)=sqrt(10)

解答

sec (\frac{θ}{5}) = 10

解答

θ = 5 \cdot 1.24904 \dots + 10 πn, θ = 10 π - 5 \cdot 1.24904 \dots + 10 πn

+1

度数

θ = 357.82525 \dots^{\circ} + 180 0^{\circ} n, θ = 1442.17474 \dots^{\circ} + 180 0^{\circ} n

求解步骤

sec (\frac{θ}{5}) = 10

使用反三角函数性质

sec (\frac{θ}{5}) = 10

sec (\frac{θ}{5}) = 10

的通解

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

\frac{θ}{5} = arcsec (10) + 2 πn, \frac{θ}{5} = 2 π - arcsec (10) + 2 πn

\frac{θ}{5} = arcsec (10) + 2 πn, \frac{θ}{5} = 2 π - arcsec (10) + 2 πn

解

\frac{θ}{5} = arcsec (10) + 2 πn : θ = 5 arcsec (10) + 10 πn

\frac{θ}{5} = arcsec (10) + 2 πn

在两边乘以

5

\frac{θ}{5} = arcsec (10) + 2 πn

在两边乘以

5

\frac{5 θ}{5} = 5 arcsec (10) + 5 \cdot 2 πn

化简

\frac{5 θ}{5} = 5 arcsec (10) + 5 \cdot 2 πn

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

5 arcsec (10) + 5 \cdot 2 πn : 5 arcsec (10) + 10 πn

5 arcsec (10) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 5 arcsec (10) + 10 πn

θ = 5 arcsec (10) + 10 πn

θ = 5 arcsec (10) + 10 πn

θ = 5 arcsec (10) + 10 πn

解

\frac{θ}{5} = 2 π - arcsec (10) + 2 πn : θ = 10 π - 5 arcsec (10) + 10 πn

\frac{θ}{5} = 2 π - arcsec (10) + 2 πn

在两边乘以

5

\frac{θ}{5} = 2 π - arcsec (10) + 2 πn

在两边乘以

5

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

化简

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn : 10 π - 5 arcsec (10) + 10 πn

5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

数字相乘:

5 \cdot 2 = 10

= 10 π - 5 arcsec (10) + 10 πn

θ = 10 π - 5 arcsec (10) + 10 πn

θ = 10 π - 5 arcsec (10) + 10 πn

θ = 10 π - 5 arcsec (10) + 10 πn

θ = 5 arcsec (10) + 10 πn, θ = 10 π - 5 arcsec (10) + 10 πn

以小数形式表示解

θ = 5 \cdot 1.24904 \dots + 10 πn, θ = 10 π - 5 \cdot 1.24904 \dots + 10 πn

作图

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