ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

csc(x)tan(x)=(2sqrt(3))/3

解

csc (x) tan (x) = \frac{2 3}{3}

解

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

+1

度

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

解答ステップ

csc (x) tan (x) = \frac{2 3}{3}

両辺から

\frac{2 3}{3}

を引く

csc (x) tan (x) - \frac{2}{3} = 0

簡素化

csc (x) tan (x) - \frac{2}{3} : \frac{3 csc ( x ) tan ( x ) - 2}{3}

csc (x) tan (x) - \frac{2}{3}

元を分数に変換する:

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

= \frac{csc ( x ) tan ( x ) 3}{3} - \frac{2}{3}

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{csc ( x ) tan ( x ) 3 - 2}{3}

\frac{3 csc ( x ) tan ( x ) - 2}{3} = 0

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

3 csc (x) tan (x) - 2 = 0

サイン, コサインで表わす

- 2 + csc (x) 3 tan (x)

基本的な三角関数の公式を使用する:

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

= - 2 + \frac{1}{sin ( x )} 3 tan (x)

基本的な三角関数の公式を使用する:

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

= - 2 + \frac{1}{sin ( x )} 3 \frac{sin ( x )}{cos ( x )}

簡素化

- 2 + \frac{1}{sin ( x )} 3 \frac{sin ( x )}{cos ( x )} : \frac{- 2 cos ( x ) + 3}{cos ( x )}

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

\frac{1}{sin ( x )} 3 \frac{sin ( x )}{cos ( x )} = \frac{3}{cos ( x )}

\frac{1}{sin ( x )} 3 \frac{sin ( x )}{cos ( x )}

分数を乗じる:

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

= \frac{1 \cdot sin ( x ) 3}{sin ( x ) cos ( x )}

共通因数を約分する:

sin (x)

= \frac{1 \cdot 3}{cos ( x )}

乗算:

1 \cdot 3 = 3

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

= - 2 + \frac{3}{cos ( x )}

元を分数に変換する:

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

= - \frac{2 cos ( x )}{cos ( x )} + \frac{3}{cos ( 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 cos ( x ) + 3}{cos ( x )}

= \frac{- 2 cos ( x ) + 3}{cos ( x )}

\frac{3 - 2 cos ( x )}{cos ( x )} = 0

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

3 - 2 cos (x) = 0

3

を右側に移動します

3 - 2 cos (x) = 0

両辺から

3

を引く

3 - 2 cos (x) - 3 = 0 - 3

簡素化

- 2 cos (x) = - 3

- 2 cos (x) = - 3

以下で両辺を割る

- 2

- 2 cos (x) = - 3

以下で両辺を割る

- 2

\frac{- 2 cos ( x )}{- 2} = \frac{- 3}{- 2}

簡素化

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

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

以下の一般解

cos (x) = \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}

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

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

グラフ

人気の例

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

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

cos^2(2x)-1/4 =0

cos^{2} (2 x) - \frac{1}{4} = 0

solvefor c,1=tan(c)

so l v e f or c, 1 = tan (c)

4cos^2(x)+3sin^2(x)-4=-tan^2(x)

4 cos^{2} (x) + 3 sin^{2} (x) - 4 = - tan^{2} (x)

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

tan^{2} (x) - 2 = 3 tan (x)