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人気のある三角関数 >

sin(x)cos(x)=-1/4 ,0<= x<= 2pi

解

sin (x) cos (x) = - \frac{1}{4}, 0 \leq x \leq 2 π

解

x = \frac{7 π}{12}, x = \frac{11 π}{12}, x = \frac{19 π}{12}, x = \frac{23 π}{12}

+1

度

x = 10 5^{\circ}, x = 16 5^{\circ}, x = 28 5^{\circ}, x = 34 5^{\circ}

解答ステップ

sin (x) cos (x) = - \frac{1}{4}, 0 \leq x \leq 2 π

三角関数の公式を使用して書き換える

sin (x) cos (x)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

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

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

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

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

簡素化

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

簡素化

\frac{2 sin ( 2 x )}{2} : sin (2 x)

\frac{2 sin ( 2 x )}{2}

数を割る:

\frac{2}{2} = 1

= sin (2 x)

簡素化

2 (- \frac{1}{4}) : - \frac{1}{2}

2 (- \frac{1}{4})

括弧を削除する:

(- a) = - a

= - 2 \cdot \frac{1}{4}

分数を乗じる:

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

= - \frac{1 \cdot 2}{4}

数を乗じる:

1 \cdot 2 = 2

= - \frac{2}{4}

共通因数を約分する:

2

= - \frac{1}{2}

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

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

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

以下の一般解

sin (2 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}

2 x = \frac{7 π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

2 x = \frac{7 π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

解く

2 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{12} + πn

2 x = \frac{7 π}{6} + 2 πn

以下で両辺を割る

2

2 x = \frac{7 π}{6} + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{\frac{7 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} = \frac{\frac{7 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{\frac{7 π}{6}}{2} + \frac{2 πn}{2} : \frac{7 π}{12} + πn

\frac{\frac{7 π}{6}}{2} + \frac{2 πn}{2}

\frac{\frac{7 π}{6}}{2} = \frac{7 π}{12}

\frac{\frac{7 π}{6}}{2}

分数の規則を適用する:

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

= \frac{7 π}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= \frac{7 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

x = \frac{7 π}{12} + πn

解く

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

2 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

2

2 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

2

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

簡素化

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

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

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

x = \frac{11 π}{12} + πn

x = \frac{11 π}{12} + πn

x = \frac{11 π}{12} + πn

x = \frac{7 π}{12} + πn, x = \frac{11 π}{12} + πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{7 π}{12}, x = \frac{11 π}{12}, x = \frac{19 π}{12}, x = \frac{23 π}{12}

グラフ

人気の例

tan (x) = (\frac{4}{3})

4sin^2(x)+4cos(2x)=1

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

cot(θ)=4,cos(θ)<0

cot (θ) = 4, cos (θ) < 0

(tan(x)+1)(sin(x)-1)=0

(tan (x) + 1) (sin (x) - 1) = 0

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