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人気のある三角関数 >

sec(x/5)=sqrt(10)

解

sec (\frac{x}{5}) = 10

解

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

+1

度

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

解答ステップ

sec (\frac{x}{5}) = 10

三角関数の逆数プロパティを適用する

sec (\frac{x}{5}) = 10

以下の一般解

sec (\frac{x}{5}) = 10

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

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

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

解く

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

\frac{x}{5} = arcsec (10) + 2 πn

以下で両辺を乗じる:

5

\frac{x}{5} = arcsec (10) + 2 πn

以下で両辺を乗じる:

5

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

簡素化

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

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

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

5 arcsec (10) + 5 \cdot 2 πn

数を乗じる:

5 \cdot 2 = 10

= 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

解く

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

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

以下で両辺を乗じる:

5

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

以下で両辺を乗じる:

5

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

簡素化

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

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

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

数を乗じる:

5 \cdot 2 = 10

= 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

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

10進法形式で解を証明する

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

グラフ

人気の例

csc (x) = - 3

csc (x) = - 5

csc^2(θ)+1=cot^2(θ)

csc^{2} (θ) + 1 = cot^{2} (θ)

csc^{2} (θ) = 1

sin^2(θ)=cos^2(θ)-1

sin^{2} (θ) = cos^{2} (θ) - 1