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人気のある三角関数 >

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

解

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

両辺から

sec (x)

を引く

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

簡素化

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

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

元を分数に変換する:

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

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

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

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

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

三角関数の公式を使用して書き換える

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

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

因数

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

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

指数の規則を適用する:

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

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

= sin (x) - sin (x) sin (x)

共通項をくくり出す

sin (x)

= sin (x) (1 - sec (x) sin (x))

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

各部分を別個に解く

sin (x) = 0 or 1 - sec (x) sin (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

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

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

三角関数の公式を使用して書き換える

1 - sec (x) sin (x)

sec (x) sin (x) = tan (x)

sec (x) sin (x)

サイン, コサインで表わす

sec (x) sin (x)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

分数を乗じる:

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

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

乗算:

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

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

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

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

基本的な三角関数の公式を使用する:

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

= tan (x)

= 1 - tan (x)

1 - tan (x) = 0

1

を右側に移動します

1 - tan (x) = 0

両辺から

1

を引く

1 - tan (x) - 1 = 0 - 1

簡素化

- tan (x) = - 1

- tan (x) = - 1

以下で両辺を割る

- 1

- tan (x) = - 1

以下で両辺を割る

- 1

\frac{- tan ( x )}{- 1} = \frac{- 1}{- 1}

簡素化

tan (x) = 1

tan (x) = 1

以下の一般解

tan (x) = 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{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(2x)-2sin(x)=1,0<x<= 360

cos (2 x) - 2 sin (x) = 1, 0^{\circ} < x \leq 36 0^{\circ}

cos (aπ) - 1 = 0

3tan(2θ)-sqrt(3)=0

3 tan (2 θ) - 3 = 0

cos(θ)=(4k-1)/3

cos (θ) = \frac{4 k - 1}{3}

5 sin (x) - 4 = 0