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人気のある三角関数 >

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

解

4 cot (x) = 3 csc (x)

解

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

+1

度

x = 64.34109 \dots^{\circ} + 36 0^{\circ} n, x = 295.65890 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

4 cot (x) = 3 csc (x)

両辺から

3 csc (x)

を引く

4 cot (x) - 3 csc (x) = 0

サイン, コサインで表わす

4 cot (x) - csc (x) 3

基本的な三角関数の公式を使用する:

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

= 4 \cdot \frac{cos ( x )}{sin ( x )} - csc (x) 3

基本的な三角関数の公式を使用する:

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

= 4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3

簡素化

4 \cdot \frac{cos ( x )}{sin ( x )} - \frac{1}{sin ( x )} 3 : \frac{4 cos ( x ) - 3}{sin ( x )}

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

4 \cdot \frac{cos ( x )}{sin ( x )} = \frac{4 cos ( x )}{sin ( x )}

4 \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 4}{sin ( x )}

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

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

分数を乗じる:

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

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

乗算:

1 \cdot 3 = 3

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

= \frac{4 cos ( x )}{sin ( x )} - \frac{3}{sin ( x )}

規則を適用

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

= \frac{4 cos ( x ) - 3}{sin ( x )}

= \frac{4 cos ( x ) - 3}{sin ( x )}

\frac{- 3 + 4 cos ( x )}{sin ( x )} = 0

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

- 3 + 4 cos (x) = 0

3

を右側に移動します

- 3 + 4 cos (x) = 0

両辺に

3

を足す

- 3 + 4 cos (x) + 3 = 0 + 3

簡素化

4 cos (x) = 3

4 cos (x) = 3

以下で両辺を割る

4

4 cos (x) = 3

以下で両辺を割る

4

\frac{4 cos ( x )}{4} = \frac{3}{4}

簡素化

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

三角関数の逆数プロパティを適用する

cos (x) = \frac{3}{4}

以下の一般解

cos (x) = \frac{3}{4}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

10進法形式で解を証明する

x = 1.12296 \dots + 2 πn, x = 2 π - 1.12296 \dots + 2 πn

グラフ

人気の例

sin (θ) = \frac{7}{15}

cos(x)=(sqrt(5))/3

cos (x) = \frac{5}{3}

cos (x) = - \frac{7}{8}

sin(x)=-cos(2x)

sin (x) = - cos (2 x)

csc(pi/(24)x)=1

csc (\frac{π}{24} x) = 1