ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

50sin^2(x)=50+25cos(x)

解

50 sin^{2} (x) = 50 + 25 cos (x)

解

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

度

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n, x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

解答ステップ

50 sin^{2} (x) = 50 + 25 cos (x)

両辺から

50 + 25 cos (x)

を引く

50 sin^{2} (x) - 50 - 25 cos (x) = 0

三角関数の公式を使用して書き換える

- 50 - 25 cos (x) + 50 sin^{2} (x)

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

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

= - 50 - 25 cos (x) + 50 (1 - cos^{2} (x))

簡素化

- 50 - 25 cos (x) + 50 (1 - cos^{2} (x)) : - 50 cos^{2} (x) - 25 cos (x)

- 50 - 25 cos (x) + 50 (1 - cos^{2} (x))

拡張

50 (1 - cos^{2} (x)) : 50 - 50 cos^{2} (x)

50 (1 - cos^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 50, b = 1, c = cos^{2} (x)

= 50 \cdot 1 - 50 cos^{2} (x)

数を乗じる:

50 \cdot 1 = 50

= 50 - 50 cos^{2} (x)

= - 50 - 25 cos (x) + 50 - 50 cos^{2} (x)

簡素化

- 50 - 25 cos (x) + 50 - 50 cos^{2} (x) : - 50 cos^{2} (x) - 25 cos (x)

- 50 - 25 cos (x) + 50 - 50 cos^{2} (x)

条件のようなグループ

= - 25 cos (x) - 50 cos^{2} (x) - 50 + 50

- 50 + 50 = 0

= - 50 cos^{2} (x) - 25 cos (x)

= - 50 cos^{2} (x) - 25 cos (x)

= - 50 cos^{2} (x) - 25 cos (x)

- 25 cos (x) - 50 cos^{2} (x) = 0

置換で解く

- 25 cos (x) - 50 cos^{2} (x) = 0

仮定:

cos (x) = u

- 25 u - 50 u^{2} = 0

- 25 u - 50 u^{2} = 0 : u = - \frac{1}{2}, u = 0

- 25 u - 50 u^{2} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

- 50 u^{2} - 25 u = 0

解くとthe二次式

- 50 u^{2} - 25 u = 0

二次Equationの公式:

次の場合:

a = - 50, b = - 25, c = 0

u_{1, 2} = \frac{- ( - 25 ) \pm ( - 25 ) ^{2} - 4 ( - 50 ) \cdot 0}{2 ( - 50 )}

u_{1, 2} = \frac{- ( - 25 ) \pm ( - 25 ) ^{2} - 4 ( - 50 ) \cdot 0}{2 ( - 50 )}

(- 25)^{2} - 4 (- 50) \cdot 0 = 25

(- 25)^{2} - 4 (- 50) \cdot 0

規則を適用

- (- a) = a

= (- 25)^{2} + 4 \cdot 50 \cdot 0

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 25)^{2} = 2 5^{2}

= 2 5^{2} + 4 \cdot 50 \cdot 0

規則を適用

0 \cdot a = 0

= 2 5^{2} + 0

2 5^{2} + 0 = 2 5^{2}

= 2 5^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

= 25

u_{1, 2} = \frac{- ( - 25 ) \pm 25}{2 ( - 50 )}

解を分離する

u_{1} = \frac{- ( - 25 ) + 25}{2 ( - 50 )}, u_{2} = \frac{- ( - 25 ) - 25}{2 ( - 50 )}

u = \frac{- ( - 25 ) + 25}{2 ( - 50 )} : - \frac{1}{2}

\frac{- ( - 25 ) + 25}{2 ( - 50 )}

括弧を削除する:

(- a) = - a, - (- a) = a

= \frac{25 + 25}{- 2 \cdot 50}

数を足す:

25 + 25 = 50

= \frac{50}{- 2 \cdot 50}

数を乗じる:

2 \cdot 50 = 100

= \frac{50}{- 100}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{50}{100}

共通因数を約分する:

50

= - \frac{1}{2}

u = \frac{- ( - 25 ) - 25}{2 ( - 50 )} : 0

\frac{- ( - 25 ) - 25}{2 ( - 50 )}

括弧を削除する:

(- a) = - a, - (- a) = a

= \frac{25 - 25}{- 2 \cdot 50}

数を引く:

25 - 25 = 0

= \frac{0}{- 2 \cdot 50}

数を乗じる:

2 \cdot 50 = 100

= \frac{0}{- 100}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{0}{100}

規則を適用

\frac{0}{a} = 0, a \neq = 0

= - 0

= 0

二次equationの解:

u = - \frac{1}{2}, u = 0

代用を戻す

u = cos (x)

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

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

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}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

すべての解を組み合わせる

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

グラフ

人気の例

arctan (x) = π

2 cos^{2} (x) = 0

cos^2(θ)+2cos(θ)+1=0

cos^{2} (θ) + 2 cos (θ) + 1 = 0

sec^2(θ)+tan(θ)=0

sec^{2} (θ) + tan (θ) = 0

sin(x)+sqrt(3)cos(x)=2

sin (x) + 3 cos (x) = 2