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人気のある三角関数 >

2cos(12x)=sqrt(3)

解

2 cos (12 x) = 3

解

x = \frac{π}{72} + \frac{πn}{6}, x = \frac{11 π}{72} + \frac{πn}{6}

+1

度

x = 2. 5^{\circ} + 3 0^{\circ} n, x = 27. 5^{\circ} + 3 0^{\circ} n

解答ステップ

2 cos (12 x) = 3

以下で両辺を割る

2

2 cos (12 x) = 3

以下で両辺を割る

2

\frac{2 cos ( 12 x )}{2} = \frac{3}{2}

簡素化

cos (12 x) = \frac{3}{2}

cos (12 x) = \frac{3}{2}

以下の一般解

cos (12 x) = \frac{3}{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}

12 x = \frac{π}{6} + 2 πn, 12 x = \frac{11 π}{6} + 2 πn

12 x = \frac{π}{6} + 2 πn, 12 x = \frac{11 π}{6} + 2 πn

解く

12 x = \frac{π}{6} + 2 πn : x = \frac{π}{72} + \frac{πn}{6}

12 x = \frac{π}{6} + 2 πn

以下で両辺を割る

12

12 x = \frac{π}{6} + 2 πn

以下で両辺を割る

12

\frac{12 x}{12} = \frac{\frac{π}{6}}{12} + \frac{2 πn}{12}

簡素化

\frac{12 x}{12} = \frac{\frac{π}{6}}{12} + \frac{2 πn}{12}

簡素化

\frac{12 x}{12} : x

\frac{12 x}{12}

数を割る:

\frac{12}{12} = 1

= x

簡素化

\frac{\frac{π}{6}}{12} + \frac{2 πn}{12} : \frac{π}{72} + \frac{πn}{6}

\frac{\frac{π}{6}}{12} + \frac{2 πn}{12}

\frac{\frac{π}{6}}{12} = \frac{π}{72}

\frac{\frac{π}{6}}{12}

分数の規則を適用する:

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

= \frac{π}{6 \cdot 12}

数を乗じる:

6 \cdot 12 = 72

= \frac{π}{72}

\frac{2 πn}{12} = \frac{πn}{6}

\frac{2 πn}{12}

共通因数を約分する:

2

= \frac{πn}{6}

= \frac{π}{72} + \frac{πn}{6}

x = \frac{π}{72} + \frac{πn}{6}

x = \frac{π}{72} + \frac{πn}{6}

x = \frac{π}{72} + \frac{πn}{6}

解く

12 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{72} + \frac{πn}{6}

12 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

12

12 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

12

\frac{12 x}{12} = \frac{\frac{11 π}{6}}{12} + \frac{2 πn}{12}

簡素化

\frac{12 x}{12} = \frac{\frac{11 π}{6}}{12} + \frac{2 πn}{12}

簡素化

\frac{12 x}{12} : x

\frac{12 x}{12}

数を割る:

\frac{12}{12} = 1

= x

簡素化

\frac{\frac{11 π}{6}}{12} + \frac{2 πn}{12} : \frac{11 π}{72} + \frac{πn}{6}

\frac{\frac{11 π}{6}}{12} + \frac{2 πn}{12}

\frac{\frac{11 π}{6}}{12} = \frac{11 π}{72}

\frac{\frac{11 π}{6}}{12}

分数の規則を適用する:

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

= \frac{11 π}{6 \cdot 12}

数を乗じる:

6 \cdot 12 = 72

= \frac{11 π}{72}

\frac{2 πn}{12} = \frac{πn}{6}

\frac{2 πn}{12}

共通因数を約分する:

2

= \frac{πn}{6}

= \frac{11 π}{72} + \frac{πn}{6}

x = \frac{11 π}{72} + \frac{πn}{6}

x = \frac{11 π}{72} + \frac{πn}{6}

x = \frac{11 π}{72} + \frac{πn}{6}

x = \frac{π}{72} + \frac{πn}{6}, x = \frac{11 π}{72} + \frac{πn}{6}

グラフ

人気の例

7 sin (5 x) = 2

arccot(x)+arccot(1+x)= pi/4

arccot (x) + arccot (1 + x) = \frac{π}{4}

arcsin(x-0.355)=0.489

arcsin (x - 0.355) = 0.489

cos(pi/2-x)= 4/5

cos (\frac{π}{2} - x) = \frac{4}{5}

6 = 10 cos (4 \cdot o)