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人気のある三角関数 >

2cos(x/5)-sqrt(2)=0

解

2 cos (\frac{x}{5}) - 2 = 0

解

x = \frac{5 π}{4} + 10 πn, x = \frac{35 π}{4} + 10 πn

+1

度

x = 22 5^{\circ} + 180 0^{\circ} n, x = 157 5^{\circ} + 180 0^{\circ} n

解答ステップ

2 cos (\frac{x}{5}) - 2 = 0

2

を右側に移動します

2 cos (\frac{x}{5}) - 2 = 0

両辺に

2

を足す

2 cos (\frac{x}{5}) - 2 + 2 = 0 + 2

簡素化

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

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

以下で両辺を割る

2

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

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{x}{5} = \frac{π}{4} + 2 πn, \frac{x}{5} = \frac{7 π}{4} + 2 πn

\frac{x}{5} = \frac{π}{4} + 2 πn, \frac{x}{5} = \frac{7 π}{4} + 2 πn

解く

\frac{x}{5} = \frac{π}{4} + 2 πn : x = \frac{5 π}{4} + 10 πn

\frac{x}{5} = \frac{π}{4} + 2 πn

以下で両辺を乗じる:

5

\frac{x}{5} = \frac{π}{4} + 2 πn

以下で両辺を乗じる:

5

\frac{5 x}{5} = 5 \cdot \frac{π}{4} + 5 \cdot 2 πn

簡素化

\frac{5 x}{5} = 5 \cdot \frac{π}{4} + 5 \cdot 2 πn

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

5 \cdot \frac{π}{4} + 5 \cdot 2 πn : \frac{5 π}{4} + 10 πn

5 \cdot \frac{π}{4} + 5 \cdot 2 πn

乗じる

5 \cdot \frac{π}{4} : \frac{5 π}{4}

5 \cdot \frac{π}{4}

分数を乗じる:

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

= \frac{π 5}{4}

= \frac{5 π}{4} + 5 \cdot 2 πn

数を乗じる:

5 \cdot 2 = 10

= \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

解く

\frac{x}{5} = \frac{7 π}{4} + 2 πn : x = \frac{35 π}{4} + 10 πn

\frac{x}{5} = \frac{7 π}{4} + 2 πn

以下で両辺を乗じる:

5

\frac{x}{5} = \frac{7 π}{4} + 2 πn

以下で両辺を乗じる:

5

\frac{5 x}{5} = 5 \cdot \frac{7 π}{4} + 5 \cdot 2 πn

簡素化

\frac{5 x}{5} = 5 \cdot \frac{7 π}{4} + 5 \cdot 2 πn

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

5 \cdot \frac{7 π}{4} + 5 \cdot 2 πn : \frac{35 π}{4} + 10 πn

5 \cdot \frac{7 π}{4} + 5 \cdot 2 πn

5 \cdot \frac{7 π}{4} = \frac{35 π}{4}

5 \cdot \frac{7 π}{4}

分数を乗じる:

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

= \frac{7 π 5}{4}

数を乗じる:

7 \cdot 5 = 35

= \frac{35 π}{4}

5 \cdot 2 πn = 10 πn

5 \cdot 2 πn

数を乗じる:

5 \cdot 2 = 10

= 10 πn

= \frac{35 π}{4} + 10 πn

x = \frac{35 π}{4} + 10 πn

x = \frac{35 π}{4} + 10 πn

x = \frac{35 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn, x = \frac{35 π}{4} + 10 πn

グラフ

人気の例

2sin^2(x)+3=7sin(x)

25sin^2(θ)-1=0

2cos(x)sin(x)+9sin(x)=0