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人気のある三角関数 >

cos(2t)=(sqrt(3))/2

解

cos (2 t) = \frac{3}{2}

解

t = \frac{π}{12} + πn, t = \frac{11 π}{12} + πn

+1

度

t = 1 5^{\circ} + 18 0^{\circ} n, t = 16 5^{\circ} + 18 0^{\circ} n

解答ステップ

cos (2 t) = \frac{3}{2}

以下の一般解

cos (2 t) = \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}

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

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

解く

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

2 t = \frac{π}{6} + 2 πn

以下で両辺を割る

2

2 t = \frac{π}{6} + 2 πn

以下で両辺を割る

2

\frac{2 t}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 t}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 t}{2} : t

\frac{2 t}{2}

数を割る:

\frac{2}{2} = 1

= t

簡素化

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

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

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

分数の規則を適用する:

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

= \frac{π}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= \frac{π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{12} + πn

t = \frac{π}{12} + πn

t = \frac{π}{12} + πn

t = \frac{π}{12} + πn

解く

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

2 t = \frac{11 π}{6} + 2 πn

以下で両辺を割る

2

2 t = \frac{11 π}{6} + 2 πn

以下で両辺を割る

2

\frac{2 t}{2} = \frac{\frac{11 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 t}{2} = \frac{\frac{11 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 t}{2} : t

\frac{2 t}{2}

数を割る:

\frac{2}{2} = 1

= t

簡素化

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

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

\frac{\frac{11 π}{6}}{2} = \frac{11 π}{12}

\frac{\frac{11 π}{6}}{2}

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 2}

数を乗じる:

6 \cdot 2 = 12

= \frac{11 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{11 π}{12} + πn

t = \frac{11 π}{12} + πn

t = \frac{11 π}{12} + πn

t = \frac{11 π}{12} + πn

t = \frac{π}{12} + πn, t = \frac{11 π}{12} + πn

グラフ

人気の例

cos(x)=-0.3178,0<= x<= 2pi

cos (x) = - 0.3178, 0 \leq x \leq 2 π

arccos(x)= pi/3

arccos (x) = \frac{π}{3}

arccos(x)= pi/2

arccos (x) = \frac{π}{2}

tan(10x)=cot(5x)

tan (10 x) = cot (5 x)

sin(x)=(4.5)/(11.75)

sin (x) = \frac{4.5}{11.75}