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人気のある三角関数 >

csc(x)= 1/(sec(x))

解

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

解

以下の解はない : x \in R

解答ステップ

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

両辺から

\frac{1}{sec ( x )}

を引く

csc (x) - \frac{1}{sec ( x )} = 0

簡素化

csc (x) - \frac{1}{sec ( x )} : \frac{csc ( x ) sec ( x ) - 1}{sec ( x )}

csc (x) - \frac{1}{sec ( x )}

元を分数に変換する:

csc (x) = \frac{csc ( x ) sec ( x )}{sec ( x )}

= \frac{csc ( x ) sec ( x )}{sec ( x )} - \frac{1}{sec ( 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{csc ( x ) sec ( x ) - 1}{sec ( x )}

\frac{csc ( x ) sec ( x ) - 1}{sec ( x )} = 0

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

csc (x) sec (x) - 1 = 0

サイン, コサインで表わす

- 1 + csc (x) sec (x)

基本的な三角関数の公式を使用する:

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

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

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

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

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

数を乗じる:

1 \cdot 1 = 1

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

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

元を分数に変換する:

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

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

乗算:

1 \cdot sin (x) = sin (x)

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

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

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

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

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

三角関数の公式を使用して書き換える

1 - cos (x) sin (x)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

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

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

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

1

を右側に移動します

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

両辺から

1

を引く

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

簡素化

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

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

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

簡素化

- sin (2 x) = - 2

- sin (2 x) = - 2

以下で両辺を割る

- 1

- sin (2 x) = - 2

以下で両辺を割る

- 1

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

簡素化

sin (2 x) = 2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

以下の解はない : x \in R

グラフ

人気の例

tan (2 θ) = 0.55

35.35=100cos(x)

35.35 = 100 cos (x)

sin (θ) = - \frac{3}{8}

sin(2x-20)=-cos(3x+50)

sin (2 x - 20) = - cos (3 x + 50)

(sin(60))/(174.36)=(sin(x))/(200)

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}