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人気のある三角関数 >

sec(2x-10)=csc(50)

解

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

解

x = 18 0^{\circ} n + 5^{\circ} + \frac{0.69813 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{0.69813 \dots}{2}

+1

ラジアン

x = \frac{π}{36} + \frac{0.69813 \dots}{2} + πn, x = π + \frac{π}{36} - \frac{0.69813 \dots}{2} + πn

解答ステップ

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

三角関数の逆数プロパティを適用する

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

以下の一般解

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

sec (x) = a \Rightarrow x = arcsec (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arcsec (a) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

解く

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

両辺に

1 0^{\circ}

を足す

2 x - 1 0^{\circ} + 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

簡素化

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

\frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{18 \cdot 2}

数を乗じる:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

解く

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

両辺に

1 0^{\circ}

を足す

2 x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

簡素化

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

条件のようなグループ

= 18 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

18 0^{\circ} = 18 0^{\circ}

18 0^{\circ}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{18 \cdot 2}

数を乗じる:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

10進法形式で解を証明する

x = 18 0^{\circ} n + 5^{\circ} + \frac{0.69813 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{0.69813 \dots}{2}

グラフ

人気の例

7sec(x)-7=0,0<= x<= 2pi

7 sec (x) - 7 = 0, 0 \leq x \leq 2 π

cos(x)+cos(x)=cos(2x)

cos (x) + cos (x) = cos (2 x)

csc^2(2x-0.6)=16

csc^{2} (2 x - 0.6) = 16

tan (x - 1) = 2

5sin^2(x)+10sin(x)+2=0

5 sin^{2} (x) + 10 sin (x) + 2 = 0