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人気のある三角関数 >

tan(x)csc(x)=2

解

tan (x) csc (x) = 2

解

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

+1

度

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

tan (x) csc (x) = 2

両辺から

2

を引く

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

サイン, コサインで表わす

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

簡素化

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

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

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

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

分数を乗じる:

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

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

共通因数を約分する:

sin (x)

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

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

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

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

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

1 - 2 cos (x) = 0

1

を右側に移動します

1 - 2 cos (x) = 0

両辺から

1

を引く

1 - 2 cos (x) - 1 = 0 - 1

簡素化

- 2 cos (x) = - 1

- 2 cos (x) = - 1

以下で両辺を割る

- 2

- 2 cos (x) = - 1

以下で両辺を割る

- 2

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

簡素化

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

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

以下の一般解

cos (x) = \frac{1}{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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

グラフ

人気の例

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

4=3-cot(x)-csc(x)

4 = 3 - cot (x) - csc (x)

7sin(x)tan(x)=3tan(x)

7 sin (x) tan (x) = 3 tan (x)

sin(2x)+cos(3x)=0

sin (2 x) + cos (3 x) = 0

2cos^2(x)+2cos(x)-1=0,0<= x<= 2pi

2 cos^{2} (x) + 2 cos (x) - 1 = 0, 0 \leq x \leq 2 π