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人気のある三角関数 >

sin(x)+cos(x)*cot(x)=2

解

sin (x) + cos (x) \cdot cot (x) = 2

解

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

度

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

解答ステップ

sin (x) + cos (x) cot (x) = 2

両辺から

2

を引く

sin (x) + cos (x) cot (x) - 2 = 0

サイン, コサインで表わす

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

簡素化

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

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

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

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

分数を乗じる:

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

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

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

cos (x) cos (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

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

= cos^{1 + 1} (x)

数を足す:

1 + 1 = 2

= cos^{2} (x)

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

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

元を分数に変換する:

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

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

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

- 2 sin (x) + sin (x) sin (x) + cos^{2} (x)

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

sin (x) sin (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

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

= sin^{1 + 1} (x)

数を足す:

1 + 1 = 2

= sin^{2} (x)

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

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

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

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

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

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

三角関数の公式を使用して書き換える

cos^{2} (x) + sin^{2} (x) - 2 sin (x)

ピタゴラスの公式を使用する:

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

= - 2 sin (x) + 1

- 2 sin (x) + 1 = 0

1

を右側に移動します

- 2 sin (x) + 1 = 0

両辺から

1

を引く

- 2 sin (x) + 1 - 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{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

グラフ

人気の例

tan (θ) = \frac{6}{12}

8 cos (x + 1 0^{\circ}) = 5

tan (x) = 1.33

cot (x) = 5

8^2=14^2+19^2-2(14)(19)cos(C)

8^{2} = 1 4^{2} + 1 9^{2} - 2 (14) (19) cos (C)