ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

8cos(3x)=2

解

8 cos (3 x) = 2

解

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

+1

度

x = 25.17416 \dots^{\circ} + 12 0^{\circ} n, x = 94.82583 \dots^{\circ} + 12 0^{\circ} n

解答ステップ

8 cos (3 x) = 2

以下で両辺を割る

8

8 cos (3 x) = 2

以下で両辺を割る

8

\frac{8 cos ( 3 x )}{8} = \frac{2}{8}

簡素化

cos (3 x) = \frac{1}{4}

cos (3 x) = \frac{1}{4}

三角関数の逆数プロパティを適用する

cos (3 x) = \frac{1}{4}

以下の一般解

cos (3 x) = \frac{1}{4}

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

3 x = arccos (\frac{1}{4}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

3 x = arccos (\frac{1}{4}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

解く

3 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{1}{4}) + 2 πn

以下で両辺を割る

3

3 x = arccos (\frac{1}{4}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

解く

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

以下で両辺を割る

3

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

10進法形式で解を証明する

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

グラフ

人気の例

tan(x/2)=(4-pi)/pi

tan (\frac{x}{2}) = \frac{4 - π}{π}

sin^2(x)=sin^2(x)sec(x)

sin^{2} (x) = sin^{2} (x) sec (x)

sin(x)=(4.2)/(9.5)

sin (x) = \frac{4.2}{9.5}

cos(x)=(4.6)/(8.6)

cos (x) = \frac{4.6}{8.6}

5tan(x)+5tan^2(x)=0

5 tan (x) + 5 tan^{2} (x) = 0