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人気のある三角関数 >

cos(x/2)= 5/6

解

cos (\frac{x}{2}) = \frac{5}{6}

解

x = 2 \cdot 0.58568 \dots + 4 πn, x = 4 π - 2 \cdot 0.58568 \dots + 4 πn

+1

度

x = 67.11461 \dots^{\circ} + 72 0^{\circ} n, x = 652.88538 \dots^{\circ} + 72 0^{\circ} n

解答ステップ

cos (\frac{x}{2}) = \frac{5}{6}

三角関数の逆数プロパティを適用する

cos (\frac{x}{2}) = \frac{5}{6}

以下の一般解

cos (\frac{x}{2}) = \frac{5}{6}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

解く

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn : x = 2 arccos (\frac{5}{6}) + 4 πn

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} = 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 arccos (\frac{5}{6}) + 2 \cdot 2 πn : 2 arccos (\frac{5}{6}) + 4 πn

2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn

解く

\frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn : x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

\frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} = 2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{5}{6}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{5}{6}) + 4 πn

x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn, x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

10進法形式で解を証明する

x = 2 \cdot 0.58568 \dots + 4 πn, x = 4 π - 2 \cdot 0.58568 \dots + 4 πn

グラフ

人気の例

sin (B) = \frac{9}{16}

(sin(118))/(18.03)=(sin(b))/(17)

\frac{sin ( 11 8 ^{\circ} )}{18.03} = \frac{sin ( b ^{\circ} )}{17}

45=57.7+arctan((3.5)/x)-arctan((175)/x)

4 5^{\circ} = 57. 7^{\circ} + arctan (\frac{3.5}{x}) - arctan (\frac{175}{x})

\frac{1}{2} - cos (\frac{x}{2}) = 0

tan(θ)=(2pi)/3

tan (θ) = \frac{2 π}{3}