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人気のある三角関数 >

sin(A)-0.6*cos(A)=(2.77)/(9.8)

解

sin (A) - 0.6 \cdot cos (A) = \frac{2.77}{9.8}

解

A = - 2.84598 \dots + 2 πn, A = 0.78523 \dots + 2 πn

+1

度

A = - 163.06288 \dots^{\circ} + 36 0^{\circ} n, A = 44.99039 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

両辺に

0.6 cos (A)

を足す

sin (A) = 0.28265 \dots + 0.6 cos (A)

両辺を2乗する

sin^{2} (A) = (0.28265 \dots + 0.6 cos (A))^{2}

両辺から

(0.28265 \dots + 0.6 cos (A))^{2}

を引く

sin^{2} (A) - 0.07989 \dots - 0.33918 \dots cos (A) - 0.36 cos^{2} (A) = 0

三角関数の公式を使用して書き換える

- 0.07989 \dots + sin^{2} (A) - 0.33918 \dots cos (A) - 0.36 cos^{2} (A)

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)

= - 0.07989 \dots + 1 - cos^{2} (A) - 0.33918 \dots cos (A) - 0.36 cos^{2} (A)

簡素化

- 0.07989 \dots + 1 - cos^{2} (A) - 0.33918 \dots cos (A) - 0.36 cos^{2} (A) : - 1.36 cos^{2} (A) - 0.33918 \dots cos (A) + 0.92010 \dots

- 0.07989 \dots + 1 - cos^{2} (A) - 0.33918 \dots cos (A) - 0.36 cos^{2} (A)

条件のようなグループ

= - cos^{2} (A) - 0.33918 \dots cos (A) - 0.36 cos^{2} (A) - 0.07989 \dots + 1

類似した元を足す:

- cos^{2} (A) - 0.36 cos^{2} (A) = - 1.36 cos^{2} (A)

= - 1.36 cos^{2} (A) - 0.33918 \dots cos (A) - 0.07989 \dots + 1

数を足す/引く:

- 0.07989 \dots + 1 = 0.92010 \dots

= - 1.36 cos^{2} (A) - 0.33918 \dots cos (A) + 0.92010 \dots

= - 1.36 cos^{2} (A) - 0.33918 \dots cos (A) + 0.92010 \dots

0.92010 \dots - 0.33918 \dots cos (A) - 1.36 cos^{2} (A) = 0

置換で解く

0.92010 \dots - 0.33918 \dots cos (A) - 1.36 cos^{2} (A) = 0

仮定:

cos (A) = u

0.92010 \dots - 0.33918 \dots u - 1.36 u^{2} = 0

0.92010 \dots - 0.33918 \dots u - 1.36 u^{2} = 0 : u = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}, u = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

0.92010 \dots - 0.33918 \dots u - 1.36 u^{2} = 0

標準的な形式で書く

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

- 1.36 u^{2} - 0.33918 \dots u + 0.92010 \dots = 0

解くとthe二次式

- 1.36 u^{2} - 0.33918 \dots u + 0.92010 \dots = 0

二次Equationの公式:

次の場合:

a = - 1.36, b = - 0.33918 \dots, c = 0.92010 \dots

u_{1, 2} = \frac{- ( - 0.33918 \dots ) \pm ( - 0.33918 \dots ) ^{2} - 4 ( - 1.36 ) \cdot 0.92010 \dots}{2 ( - 1.36 )}

u_{1, 2} = \frac{- ( - 0.33918 \dots ) \pm ( - 0.33918 \dots ) ^{2} - 4 ( - 1.36 ) \cdot 0.92010 \dots}{2 ( - 1.36 )}

(- 0.33918 \dots)^{2} - 4 (- 1.36) \cdot 0.92010 \dots = 5.12042 \dots

(- 0.33918 \dots)^{2} - 4 (- 1.36) \cdot 0.92010 \dots

規則を適用

- (- a) = a

= (- 0.33918 \dots)^{2} + 4 \cdot 1.36 \cdot 0.92010 \dots

指数の規則を適用する:

n

が偶数であれば

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

(- 0.33918 \dots)^{2} = 0.33918 \dots^{2}

= 0.33918 \dots^{2} + 4 \cdot 0.92010 \dots \cdot 1.36

数を乗じる:

4 \cdot 1.36 \cdot 0.92010 \dots = 5.00538 \dots

= 0.33918 \dots^{2} + 5.00538 \dots

0.33918 \dots^{2} = 0.11504 \dots

= 0.11504 \dots + 5.00538 \dots

数を足す:

0.11504 \dots + 5.00538 \dots = 5.12042 \dots

= 5.12042 \dots

u_{1, 2} = \frac{- ( - 0.33918 \dots ) \pm 5.12042 \dots}{2 ( - 1.36 )}

解を分離する

u_{1} = \frac{- ( - 0.33918 \dots ) + 5.12042 \dots}{2 ( - 1.36 )}, u_{2} = \frac{- ( - 0.33918 \dots ) - 5.12042 \dots}{2 ( - 1.36 )}

u = \frac{- ( - 0.33918 \dots ) + 5.12042 \dots}{2 ( - 1.36 )} : - \frac{0.33918 \dots + 5.12042 \dots}{2.72}

\frac{- ( - 0.33918 \dots ) + 5.12042 \dots}{2 ( - 1.36 )}

括弧を削除する:

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

= \frac{0.33918 \dots + 5.12042 \dots}{- 2 \cdot 1.36}

数を乗じる:

2 \cdot 1.36 = 2.72

= \frac{0.33918 \dots + 5.12042 \dots}{- 2.72}

分数の規則を適用する:

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

= - \frac{0.33918 \dots + 5.12042 \dots}{2.72}

u = \frac{- ( - 0.33918 \dots ) - 5.12042 \dots}{2 ( - 1.36 )} : \frac{5.12042 \dots - 0.33918 \dots}{2.72}

\frac{- ( - 0.33918 \dots ) - 5.12042 \dots}{2 ( - 1.36 )}

括弧を削除する:

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

= \frac{0.33918 \dots - 5.12042 \dots}{- 2 \cdot 1.36}

数を乗じる:

2 \cdot 1.36 = 2.72

= \frac{0.33918 \dots - 5.12042 \dots}{- 2.72}

分数の規則を適用する:

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

0.33918 \dots - 5.12042 \dots = - (5.12042 \dots - 0.33918 \dots)

= \frac{5.12042 \dots - 0.33918 \dots}{2.72}

二次equationの解:

u = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}, u = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

代用を戻す

u = cos (A)

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}, cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}, cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72} : A = arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}

三角関数の逆数プロパティを適用する

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}

以下の一般解

cos (A) = - \frac{0.33918 \dots + 5.12042 \dots}{2.72}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

A = arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn

A = arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn

cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72} : A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn, A = 2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

三角関数の逆数プロパティを適用する

cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

以下の一般解

cos (A) = \frac{5.12042 \dots - 0.33918 \dots}{2.72}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn, A = 2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn, A = 2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

すべての解を組み合わせる

A = arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn, A = 2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

元のequationに当てはめて解を検算する

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

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

arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn :

偽

arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn

挿入

n = 1

arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

の挿入向け

A = arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1

sin (arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1) - 0.6 cos (arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1) = \frac{2.77}{9.8}

改良

0.86529 \dots = 0.28265 \dots

\Rightarrow 偽

解答を確認する

- arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn :

真

- arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn

挿入

n = 1

- arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

の挿入向け

A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1

sin (- arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1) - 0.6 cos (- arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 π 1) = \frac{2.77}{9.8}

改良

0.28265 \dots = 0.28265 \dots

\Rightarrow 真

解答を確認する

arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn :

真

arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

挿入

n = 1

arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

の挿入向け

A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1

sin (arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1) - 0.6 cos (arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1) = \frac{2.77}{9.8}

改良

0.28265 \dots = 0.28265 \dots

\Rightarrow 真

解答を確認する

2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn :

偽

2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

挿入

n = 1

2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1

sin (A) - 0.6 cos (A) = \frac{2.77}{9.8}

の挿入向け

A = 2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1

sin (2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1) - 0.6 cos (2 π - arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 π 1) = \frac{2.77}{9.8}

改良

- 1.13132 \dots = 0.28265 \dots

\Rightarrow 偽

A = - arccos (- \frac{0.33918 \dots + 5.12042 \dots}{2.72}) + 2 πn, A = arccos (\frac{5.12042 \dots - 0.33918 \dots}{2.72}) + 2 πn

10進法形式で解を証明する

A = - 2.84598 \dots + 2 πn, A = 0.78523 \dots + 2 πn

グラフ

人気の例

sin (x) = - 0.397

2cos(x)*tan(x)-1=0

2 cos (x) \cdot tan (x) - 1 = 0

sin (x) = - 0.465

cos (x) = \frac{10}{17}

solvefor θ,r= 7/(1+cos(θ))

so l v e f or θ, r = \frac{7}{1 + cos ( θ )}