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人気のある三角関数 >

sec(x)cot(x)=-2

解

sec (x) cot (x) = - 2

解

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

+1

度

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

解答ステップ

sec (x) cot (x) = - 2

両辺から

- 2

を引く

sec (x) cot (x) + 2 = 0

サイン, コサインで表わす

2 + cot (x) sec (x)

基本的な三角関数の公式を使用する:

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

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

基本的な三角関数の公式を使用する:

sec (x) = \frac{1}{cos ( x )}

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

簡素化

2 + \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} : \frac{2 sin ( x ) + 1}{sin ( x )}

2 + \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} = \frac{1}{sin ( x )}

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

分数を乗じる:

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

= \frac{cos ( x ) \cdot 1}{sin ( x ) cos ( x )}

共通因数を約分する:

cos (x)

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

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

元を分数に変換する:

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

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

分母が等しいので, 分数を組み合わせる:

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

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

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

\frac{1 + 2 sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + 2 sin (x) = 0

1

を右側に移動します

1 + 2 sin (x) = 0

両辺から

1

を引く

1 + 2 sin (x) - 1 = 0 - 1

簡素化

2 sin (x) = - 1

2 sin (x) = - 1

以下で両辺を割る

2

2 sin (x) = - 1

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

sin (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}

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

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

グラフ

人気の例

- csc (x) = 1

sin(θ)=-(sqrt(7))/4

sin (θ) = - \frac{7}{4}

tan (x) = \frac{1}{1}

sin (w) = 0.79

arcsin (x) = 0.5