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 >

-5cos(x)-8.6602500000000…sin(x)=-5

解

- 5 \cdot cos (x) - 8.6602500000000 \dots \cdot sin (x) = - 5

解

x = 2 πn, x = π - 1.04719 \dots + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 119.99997 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

両辺に

8.66025 \dots sin (x)

を足す

- 5 cos (x) = - 5 + 8.66025 \dots sin (x)

両辺を2乗する

(- 5 cos (x))^{2} = (- 5 + 8.66025 \dots sin (x))^{2}

両辺から

(- 5 + 8.66025 \dots sin (x))^{2}

を引く

25 cos^{2} (x) - 25 + 86.6025 sin (x) - 74.99993 \dots sin^{2} (x) = 0

三角関数の公式を使用して書き換える

- 25 + 25 cos^{2} (x) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x)

ピタゴラスの公式を使用する:

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

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

= - 25 + 25 (1 - sin^{2} (x)) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x)

簡素化

- 25 + 25 (1 - sin^{2} (x)) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x) : 86.6025 sin (x) - 99.99993 \dots sin^{2} (x)

- 25 + 25 (1 - sin^{2} (x)) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x)

拡張

25 (1 - sin^{2} (x)) : 25 - 25 sin^{2} (x)

25 (1 - sin^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 25, b = 1, c = sin^{2} (x)

= 25 \cdot 1 - 25 sin^{2} (x)

数を乗じる:

25 \cdot 1 = 25

= 25 - 25 sin^{2} (x)

= - 25 + 25 - 25 sin^{2} (x) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x)

簡素化

- 25 + 25 - 25 sin^{2} (x) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x) : 86.6025 sin (x) - 99.99993 \dots sin^{2} (x)

- 25 + 25 - 25 sin^{2} (x) - 74.99993 \dots sin^{2} (x) + 86.6025 sin (x)

類似した元を足す:

- 25 sin^{2} (x) - 74.99993 \dots sin^{2} (x) = - 99.99993 \dots sin^{2} (x)

= - 25 + 25 - 99.99993 \dots sin^{2} (x) + 86.6025 sin (x)

- 25 + 25 = 0

= 86.6025 sin (x) - 99.99993 \dots sin^{2} (x)

= 86.6025 sin (x) - 99.99993 \dots sin^{2} (x)

= 86.6025 sin (x) - 99.99993 \dots sin^{2} (x)

86.6025 sin (x) - 99.99993 \dots sin^{2} (x) = 0

置換で解く

86.6025 sin (x) - 99.99993 \dots sin^{2} (x) = 0

仮定:

sin (x) = u

86.6025 u - 99.99993 \dots u^{2} = 0

86.6025 u - 99.99993 \dots u^{2} = 0 : u = 0, u = \frac{173.205}{199.99986 \dots}

86.6025 u - 99.99993 \dots u^{2} = 0

標準的な形式で書く

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

- 99.99993 \dots u^{2} + 86.6025 u = 0

解くとthe二次式

- 99.99993 \dots u^{2} + 86.6025 u = 0

二次Equationの公式:

次の場合:

a = - 99.99993 \dots, b = 86.6025, c = 0

u_{1, 2} = \frac{- 86.6025 \pm 86.602 5 ^{2} - 4 ( - 99.99993 \dots ) \cdot 0}{2 ( - 99.99993 \dots )}

u_{1, 2} = \frac{- 86.6025 \pm 86.602 5 ^{2} - 4 ( - 99.99993 \dots ) \cdot 0}{2 ( - 99.99993 \dots )}

86.602 5^{2} - 4 (- 99.99993 \dots) \cdot 0 = 86.6025

86.602 5^{2} - 4 (- 99.99993 \dots) \cdot 0

規則を適用

- (- a) = a

= 86.602 5^{2} + 4 \cdot 99.99993 \dots \cdot 0

規則を適用

0 \cdot a = 0

= 86.602 5^{2} + 0

86.602 5^{2} + 0 = 86.602 5^{2}

= 86.602 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

= 86.6025

u_{1, 2} = \frac{- 86.6025 \pm 86.6025}{2 ( - 99.99993 \dots )}

解を分離する

u_{1} = \frac{- 86.6025 + 86.6025}{2 ( - 99.99993 \dots )}, u_{2} = \frac{- 86.6025 - 86.6025}{2 ( - 99.99993 \dots )}

u = \frac{- 86.6025 + 86.6025}{2 ( - 99.99993 \dots )} : 0

\frac{- 86.6025 + 86.6025}{2 ( - 99.99993 \dots )}

括弧を削除する:

(- a) = - a

= \frac{- 86.6025 + 86.6025}{- 2 \cdot 99.99993 \dots}

数を足す/引く:

- 86.6025 + 86.6025 = 0

= \frac{0}{- 2 \cdot 99.99993 \dots}

数を乗じる:

2 \cdot 99.99993 \dots = 199.99986 \dots

= \frac{0}{- 199.99986 \dots}

分数の規則を適用する:

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

= - \frac{0}{199.99986 \dots}

規則を適用

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

= - 0

= 0

u = \frac{- 86.6025 - 86.6025}{2 ( - 99.99993 \dots )} : \frac{173.205}{199.99986 \dots}

\frac{- 86.6025 - 86.6025}{2 ( - 99.99993 \dots )}

括弧を削除する:

(- a) = - a

= \frac{- 86.6025 - 86.6025}{- 2 \cdot 99.99993 \dots}

数を引く:

- 86.6025 - 86.6025 = - 173.205

= \frac{- 173.205}{- 2 \cdot 99.99993 \dots}

数を乗じる:

2 \cdot 99.99993 \dots = 199.99986 \dots

= \frac{- 173.205}{- 199.99986 \dots}

分数の規則を適用する:

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

= \frac{173.205}{199.99986 \dots}

二次equationの解:

u = 0, u = \frac{173.205}{199.99986 \dots}

代用を戻す

u = sin (x)

sin (x) = 0, sin (x) = \frac{173.205}{199.99986 \dots}

sin (x) = 0, sin (x) = \frac{173.205}{199.99986 \dots}

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

sin (x) = \frac{173.205}{199.99986 \dots} : x = arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn, x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

sin (x) = \frac{173.205}{199.99986 \dots}

三角関数の逆数プロパティを適用する

sin (x) = \frac{173.205}{199.99986 \dots}

以下の一般解

sin (x) = \frac{173.205}{199.99986 \dots}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn, x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

x = arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn, x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn, x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

元のequationに当てはめて解を検算する

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

に当てはめて解を確認する

equationに一致しないものを削除する。

解答を確認する

2 πn :

真

2 πn

挿入

n = 1

2 π 1

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

の挿入向け

x = 2 π 1

- 5 cos (2 π 1) - 8.66025 \dots sin (2 π 1) = - 5

改良

- 5 = - 5

\Rightarrow 真

解答を確認する

π + 2 πn :

偽

π + 2 πn

挿入

n = 1

π + 2 π 1

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

の挿入向け

x = π + 2 π 1

- 5 cos (π + 2 π 1) - 8.66025 \dots sin (π + 2 π 1) = - 5

改良

5 = - 5

\Rightarrow 偽

解答を確認する

arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn :

偽

arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

挿入

n = 1

arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

の挿入向け

x = arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1

- 5 cos (arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1) - 8.66025 \dots sin (arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1) = - 5

改良

- 9.99999 \dots = - 5

\Rightarrow 偽

解答を確認する

π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn :

真

π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

挿入

n = 1

π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1

- 5 cos (x) - 8.66025 \dots sin (x) = - 5

の挿入向け

x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1

- 5 cos (π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1) - 8.66025 \dots sin (π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 π 1) = - 5

改良

- 5 = - 5

\Rightarrow 真

x = 2 πn, x = π - arcsin (\frac{173.205}{199.99986 \dots}) + 2 πn

10進法形式で解を証明する

x = 2 πn, x = π - 1.04719 \dots + 2 πn

グラフ

人気の例

cos(x)= 2/(sqrt(5))

cos (x) = \frac{2}{5}

tan(x/2-pi/4)=sqrt(3)

tan (\frac{x}{2} - \frac{π}{4}) = 3

5sqrt(3)tan(x)+5=0

53 tan (x) + 5 = 0

2 cot^{2} (x) = 6

sin (x) = 0.3456