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人気のある三角関数 >

sqrt(2)sec(x)-3tan(x)=-tan(x)

解

2 sec (x) - 3 tan (x) = - tan (x)

解

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

+1

度

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

解答ステップ

2 sec (x) - 3 tan (x) = - tan (x)

両辺から

- tan (x)

を引く

2 sec (x) - 2 tan (x) = 0

サイン, コサインで表わす

- 2 tan (x) + sec (x) 2

基本的な三角関数の公式を使用する:

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

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

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

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

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

分数を乗じる:

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

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

\frac{1}{cos ( x )} 2 = \frac{2}{cos ( x )}

\frac{1}{cos ( x )} 2

分数を乗じる:

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

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

乗算:

1 \cdot 2 = 2

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

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

規則を適用

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

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

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

\frac{2 - 2 sin ( x )}{cos ( x )} = 0

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

2 - 2 sin (x) = 0

2

を右側に移動します

2 - 2 sin (x) = 0

両辺から

2

を引く

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

簡素化

- 2 sin (x) = - 2

- 2 sin (x) = - 2

以下で両辺を割る

- 2

- 2 sin (x) = - 2

以下で両辺を割る

- 2

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

簡素化

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

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

以下の一般解

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

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

グラフ

人気の例

cot(θ)+csc(θ)=-sqrt(3)

3tan^2(θ)+1= 2/(tan^2(θ))

4tan(x)=2sec^2(x)

sin(x)+cos(x)+cot(x)=csc(x)

cos^2(x)+cos(x)=cos(2x)