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人気のある三角関数 >

2sin^2(4x)=1

解

2 sin^{2} (4 x) = 1

解

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}, x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

+1

度

x = 11.2 5^{\circ} + 9 0^{\circ} n, x = 33.7 5^{\circ} + 9 0^{\circ} n, x = 56.2 5^{\circ} + 9 0^{\circ} n, x = 78.7 5^{\circ} + 9 0^{\circ} n

解答ステップ

2 sin^{2} (4 x) = 1

置換で解く

2 sin^{2} (4 x) = 1

仮定:

sin (4 x) = u

2 u^{2} = 1

2 u^{2} = 1 : u = \frac{1}{2}, u = - \frac{1}{2}

2 u^{2} = 1

以下で両辺を割る

2

2 u^{2} = 1

以下で両辺を割る

2

\frac{2 u ^{2}}{2} = \frac{1}{2}

簡素化

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{1}{2}, u = - \frac{1}{2}

代用を戻す

u = sin (4 x)

sin (4 x) = \frac{1}{2}, sin (4 x) = - \frac{1}{2}

sin (4 x) = \frac{1}{2}, sin (4 x) = - \frac{1}{2}

sin (4 x) = \frac{1}{2} : x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

sin (4 x) = \frac{1}{2}

以下の一般解

sin (4 x) = \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

4 x = \frac{π}{4} + 2 πn, 4 x = \frac{3 π}{4} + 2 πn

4 x = \frac{π}{4} + 2 πn, 4 x = \frac{3 π}{4} + 2 πn

解く

4 x = \frac{π}{4} + 2 πn : x = \frac{π}{16} + \frac{πn}{2}

4 x = \frac{π}{4} + 2 πn

以下で両辺を割る

4

4 x = \frac{π}{4} + 2 πn

以下で両辺を割る

4

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

簡素化

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

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

\frac{\frac{π}{4}}{4} + \frac{2 πn}{4} : \frac{π}{16} + \frac{πn}{2}

\frac{\frac{π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

分数の規則を適用する:

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

= \frac{π}{4 \cdot 4}

数を乗じる:

4 \cdot 4 = 16

= \frac{π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

共通因数を約分する:

2

= \frac{πn}{2}

= \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

解く

4 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{2}

4 x = \frac{3 π}{4} + 2 πn

以下で両辺を割る

4

4 x = \frac{3 π}{4} + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

簡素化

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

\frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4} : \frac{3 π}{16} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{3 π}{4}}{4} = \frac{3 π}{16}

\frac{\frac{3 π}{4}}{4}

分数の規則を適用する:

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

= \frac{3 π}{4 \cdot 4}

数を乗じる:

4 \cdot 4 = 16

= \frac{3 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

共通因数を約分する:

2

= \frac{πn}{2}

= \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

sin (4 x) = - \frac{1}{2} : x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

sin (4 x) = - \frac{1}{2}

以下の一般解

sin (4 x) = - \frac{1}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

解く

4 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{16} + \frac{πn}{2}

4 x = \frac{5 π}{4} + 2 πn

以下で両辺を割る

4

4 x = \frac{5 π}{4} + 2 πn

以下で両辺を割る

4

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

簡素化

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

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

\frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4} : \frac{5 π}{16} + \frac{πn}{2}

\frac{\frac{5 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{5 π}{4}}{4} = \frac{5 π}{16}

\frac{\frac{5 π}{4}}{4}

分数の規則を適用する:

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

= \frac{5 π}{4 \cdot 4}

数を乗じる:

4 \cdot 4 = 16

= \frac{5 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

共通因数を約分する:

2

= \frac{πn}{2}

= \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}

解く

4 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{16} + \frac{πn}{2}

4 x = \frac{7 π}{4} + 2 πn

以下で両辺を割る

4

4 x = \frac{7 π}{4} + 2 πn

以下で両辺を割る

4

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

簡素化

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

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

\frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4} : \frac{7 π}{16} + \frac{πn}{2}

\frac{\frac{7 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{7 π}{4}}{4} = \frac{7 π}{16}

\frac{\frac{7 π}{4}}{4}

分数の規則を適用する:

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

= \frac{7 π}{4 \cdot 4}

数を乗じる:

4 \cdot 4 = 16

= \frac{7 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

共通因数を約分する:

2

= \frac{πn}{2}

= \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{7 π}{16} + \frac{πn}{2}

x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

すべての解を組み合わせる

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}, x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

グラフ

人気の例

1*sin(x)=1.5*sin(x/2)

1 \cdot sin (x) = 1.5 \cdot sin (\frac{x}{2})

(sin(90))/5 =(sin(x))/4

\frac{sin ( 9 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}

sin (x) = - 0.2672

sin(x)= 3/(sqrt(10))

sin (x) = \frac{3}{10}

-20cos(θ)+10=0

- 20 cos (θ) + 10 = 0