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 >

(sin^2(x))/(1-cos^2(x))=cot(x)

解

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

解

x = \frac{π}{4} + πn

+1

度

x = 4 5^{\circ} + 18 0^{\circ} n

解答ステップ

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

両辺から

cot (x)

を引く

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

簡素化

\frac{sin ^{2} ( x )}{1 - cos ^{2} ( x )} - cot (x) : \frac{sin ^{2} ( x ) - cot ( x ) ( 1 - cos ^{2} ( x ) )}{1 - cos ^{2} ( x )}

\frac{sin ^{2} ( x )}{1 - cos ^{2} ( x )} - cot (x)

元を分数に変換する:

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

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

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

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

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

三角関数の公式を使用して書き換える

sin^{2} (x) - (1 - cos^{2} (x)) cot (x)

ピタゴラスの公式を使用する:

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

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

= sin^{2} (x) - cot (x) sin^{2} (x)

sin^{2} (x) - cot (x) sin^{2} (x) = 0

因数

sin^{2} (x) - cot (x) sin^{2} (x) : - sin^{2} (x) (cot (x) - 1)

sin^{2} (x) - cot (x) sin^{2} (x)

共通項をくくり出す

- sin^{2} (x)

= - sin^{2} (x) (- 1 + cot (x))

- sin^{2} (x) (cot (x) - 1) = 0

各部分を別個に解く

sin^{2} (x) = 0 or cot (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{2} (x) = 0

規則を適用

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

以下の一般解

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cot (x) - 1 = 0 : x = \frac{π}{4} + πn

cot (x) - 1 = 0

1

を右側に移動します

cot (x) - 1 = 0

両辺に

1

を足す

cot (x) - 1 + 1 = 0 + 1

簡素化

cot (x) = 1

cot (x) = 1

以下の一般解

cot (x) = 1

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

すべての解を組み合わせる

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

equationは以下で未定義のため:

2 πn, π + 2 πn

x = \frac{π}{4} + πn

グラフ

人気の例

cos^2(x)+cos^3(x)+cos^4(x)+cos^5(x)=0

cos^{2} (x) + cos^{3} (x) + cos^{4} (x) + cos^{5} (x) = 0

sin^2(x)-4sin(x)=-3

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

1+7sinh(x)=4cosh^2(x)

1 + 7 sinh (x) = 4 cosh^{2} (x)

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

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

cos^2(x)+6cos(x)+5=0

cos^{2} (x) + 6 cos (x) + 5 = 0