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人気のある三角関数 >

cos(2x)= 1/5

解

cos (2 x) = \frac{1}{5}

解

x = \frac{1.36943 \dots}{2} + πn, x = π - \frac{1.36943 \dots}{2} + πn

+1

度

x = 39.23152 \dots^{\circ} + 18 0^{\circ} n, x = 140.76847 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

cos (2 x) = \frac{1}{5}

三角関数の逆数プロパティを適用する

cos (2 x) = \frac{1}{5}

以下の一般解

cos (2 x) = \frac{1}{5}

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

2 x = arccos (\frac{1}{5}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{5}) + 2 πn

2 x = arccos (\frac{1}{5}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{5}) + 2 πn

解く

2 x = arccos (\frac{1}{5}) + 2 πn : x = \frac{arccos ( \frac{1}{5} )}{2} + πn

2 x = arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

2

2 x = arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arccos ( \frac{1}{5} )}{2} + \frac{2 πn}{2}

簡素化

x = \frac{arccos ( \frac{1}{5} )}{2} + πn

x = \frac{arccos ( \frac{1}{5} )}{2} + πn

解く

2 x = 2 π - arccos (\frac{1}{5}) + 2 πn : x = π - \frac{arccos ( \frac{1}{5} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

2

2 x = 2 π - arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{5} )}{2} + \frac{2 πn}{2}

簡素化

x = π - \frac{arccos ( \frac{1}{5} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{5} )}{2} + πn

x = \frac{arccos ( \frac{1}{5} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{5} )}{2} + πn

10進法形式で解を証明する

x = \frac{1.36943 \dots}{2} + πn, x = π - \frac{1.36943 \dots}{2} + πn

グラフ

人気の例

sin^2(θ)-1/2 =0

sin^{2} (θ) - \frac{1}{2} = 0

sin(x)-sin(x)tan(x)=0

sin (x) - sin (x) tan (x) = 0

tan (θ) = \frac{2}{10}

sin^{2} (θ) = - 1

10sec(2x)+5tan(2x)-15=0

10 sec (2 x) + 5 tan (2 x) - 15 = 0