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人気のある三角関数 >

sin^2(x)=2tan^2(x)

解

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

解

x = 2 πn, x = π + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

両辺から

2 tan^{2} (x)

を引く

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

因数

sin^{2} (x) - 2 tan^{2} (x) : (sin (x) + 2 tan (x)) (sin (x) - 2 tan (x))

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

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

を書き換え

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

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

累乗根の規則を適用する:

a = (a)^{2}

2 = (2)^{2}

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

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

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

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

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

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

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

= (sin (x) + 2 tan (x)) (sin (x) - 2 tan (x))

(sin (x) + 2 tan (x)) (sin (x) - 2 tan (x)) = 0

各部分を別個に解く

sin (x) + 2 tan (x) = 0 or sin (x) - 2 tan (x) = 0

sin (x) + 2 tan (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) + 2 tan (x) = 0

サイン, コサインで表わす

sin (x) + 2 tan (x)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

乗じる

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

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

分数を乗じる:

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

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

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

元を分数に変換する:

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

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

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

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

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

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

因数

cos (x) sin (x) + sin (x) 2 : sin (x) (cos (x) + 2)

cos (x) sin (x) + sin (x) 2

共通項をくくり出す

sin (x)

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

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

各部分を別個に解く

sin (x) = 0 or cos (x) + 2 = 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

cos (x) + 2 = 0 :

解なし

cos (x) + 2 = 0

2

を右側に移動します

cos (x) + 2 = 0

両辺から

2

を引く

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

簡素化

cos (x) = - 2

cos (x) = - 2

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

sin (x) - 2 tan (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - 2 tan (x) = 0

サイン, コサインで表わす

sin (x) - 2 tan (x)

基本的な三角関数の公式を使用する:

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

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

簡素化

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

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

乗じる

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

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

分数を乗じる:

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

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

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

元を分数に変換する:

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

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

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

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

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

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

因数

cos (x) sin (x) - sin (x) 2 : sin (x) (cos (x) - 2)

cos (x) sin (x) - sin (x) 2

共通項をくくり出す

sin (x)

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

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

各部分を別個に解く

sin (x) = 0 or cos (x) - 2 = 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

cos (x) - 2 = 0 :

解なし

cos (x) - 2 = 0

2

を右側に移動します

cos (x) - 2 = 0

両辺に

2

を足す

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

簡素化

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

解なし

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

グラフ

人気の例

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