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人気のある三角関数 >

-csc^2(x)+2csc(x)cot(x)=0

解

- csc^{2} (x) + 2 csc (x) cot (x) = 0

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

- csc^{2} (x) + 2 csc (x) cot (x) = 0

因数

- csc^{2} (x) + 2 csc (x) cot (x) : csc (x) (- csc (x) + 2 cot (x))

- csc^{2} (x) + 2 csc (x) cot (x)

指数の規則を適用する:

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

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

= - csc (x) csc (x) + 2 cot (x) csc (x)

共通項をくくり出す

csc (x)

= csc (x) (- csc (x) + 2 cot (x))

csc (x) (- csc (x) + 2 cot (x)) = 0

各部分を別個に解く

csc (x) = 0 or - csc (x) + 2 cot (x) = 0

csc (x) = 0 :

解なし

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

解なし

- csc (x) + 2 cot (x) = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

- csc (x) + 2 cot (x) = 0

サイン, コサインで表わす

- csc (x) + 2 cot (x)

基本的な三角関数の公式を使用する:

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

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

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

簡素化

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

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

乗じる

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

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

分数を乗じる:

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

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

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

規則を適用

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

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

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

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

両辺に

1

を足す

- 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

すべての解を組み合わせる

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

グラフ

人気の例

6sin(A)+3=4sin(A)+4

6 sin (A) + 3 = 4 sin (A) + 4

solvefor a,-10=sin(a)+15.2cos(a)

so l v e f or a, - 10 = sin (a) + 15.2 cos (a)

0=-6sin^2(θ)+3sin(θ)+2

0 = - 6 sin^{2} (θ) + 3 sin (θ) + 2

sin(2x+3/pi)= 1/2

sin (2 x + \frac{3}{π}) = \frac{1}{2}

sqrt(3)cot(x/3)+1=0

3 cot (\frac{x}{3}) + 1 = 0