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人気のある三角関数 >

sec(θ/5)=sqrt(7)

解

sec (\frac{θ}{5}) = 7

解

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

+1

度

θ = 338.96172 \dots^{\circ} + 180 0^{\circ} n, θ = 1461.03827 \dots^{\circ} + 180 0^{\circ} n

解答ステップ

sec (\frac{θ}{5}) = 7

三角関数の逆数プロパティを適用する

sec (\frac{θ}{5}) = 7

以下の一般解

sec (\frac{θ}{5}) = 7

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

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

解く

\frac{θ}{5} = arcsec (7) + 2 πn : θ = 5 arcsec (7) + 10 πn

\frac{θ}{5} = arcsec (7) + 2 πn

以下で両辺を乗じる:

5

\frac{θ}{5} = arcsec (7) + 2 πn

以下で両辺を乗じる:

5

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

簡素化

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

簡素化

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数を割る:

\frac{5}{5} = 1

= θ

簡素化

5 arcsec (7) + 5 \cdot 2 πn : 5 arcsec (7) + 10 πn

5 arcsec (7) + 5 \cdot 2 πn

数を乗じる:

5 \cdot 2 = 10

= 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

解く

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn : θ = 10 π - 5 arcsec (7) + 10 πn

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

以下で両辺を乗じる:

5

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

以下で両辺を乗じる:

5

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

簡素化

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

簡素化

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数を割る:

\frac{5}{5} = 1

= θ

簡素化

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn : 10 π - 5 arcsec (7) + 10 πn

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

数を乗じる:

5 \cdot 2 = 10

= 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn, θ = 10 π - 5 arcsec (7) + 10 πn

10進法形式で解を証明する

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

グラフ

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