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人気のある三角関数 >

sec(4x)-9=0

解

sec (4 x) - 9 = 0

解

x = \frac{1.45945 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.45945 \dots}{4} + \frac{πn}{2}

+1

度

x = 20.90515 \dots^{\circ} + 9 0^{\circ} n, x = 69.09484 \dots^{\circ} + 9 0^{\circ} n

解答ステップ

sec (4 x) - 9 = 0

9

を右側に移動します

sec (4 x) - 9 = 0

両辺に

9

を足す

sec (4 x) - 9 + 9 = 0 + 9

簡素化

sec (4 x) = 9

sec (4 x) = 9

三角関数の逆数プロパティを適用する

sec (4 x) = 9

以下の一般解

sec (4 x) = 9

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

4 x = arcsec (9) + 2 πn, 4 x = 2 π - arcsec (9) + 2 πn

4 x = arcsec (9) + 2 πn, 4 x = 2 π - arcsec (9) + 2 πn

解く

4 x = arcsec (9) + 2 πn : x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

4 x = arcsec (9) + 2 πn

以下で両辺を割る

4

4 x = arcsec (9) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

簡素化

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

解く

4 x = 2 π - arcsec (9) + 2 πn : x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

4 x = 2 π - arcsec (9) + 2 πn

以下で両辺を割る

4

4 x = 2 π - arcsec (9) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

簡素化

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

\frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

キャンセル

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

共通因数を約分する:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

キャンセル

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

共通因数を約分する:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

10進法形式で解を証明する

x = \frac{1.45945 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.45945 \dots}{4} + \frac{πn}{2}

グラフ

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