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人気のある三角関数 >

7cos(2x)=7sin^2(x)+5

解

7 cos (2 x) = 7 sin^{2} (x) + 5

解

x = 0.31372 \dots + 2 πn, x = π - 0.31372 \dots + 2 πn, x = - 0.31372 \dots + 2 πn, x = π + 0.31372 \dots + 2 πn

+1

度

x = 17.97528 \dots^{\circ} + 36 0^{\circ} n, x = 162.02471 \dots^{\circ} + 36 0^{\circ} n, x = - 17.97528 \dots^{\circ} + 36 0^{\circ} n, x = 197.97528 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

7 cos (2 x) = 7 sin^{2} (x) + 5

両辺から

7 sin^{2} (x) + 5

を引く

7 cos (2 x) - 7 sin^{2} (x) - 5 = 0

三角関数の公式を使用して書き換える

- 5 + 7 cos (2 x) - 7 sin^{2} (x)

2倍角の公式を使用:

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

= - 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x)

簡素化

- 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x) : - 21 sin^{2} (x) + 2

- 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x)

拡張

7 (1 - 2 sin^{2} (x)) : 7 - 14 sin^{2} (x)

7 (1 - 2 sin^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 7, b = 1, c = 2 sin^{2} (x)

= 7 \cdot 1 - 7 \cdot 2 sin^{2} (x)

簡素化

7 \cdot 1 - 7 \cdot 2 sin^{2} (x) : 7 - 14 sin^{2} (x)

7 \cdot 1 - 7 \cdot 2 sin^{2} (x)

数を乗じる:

7 \cdot 1 = 7

= 7 - 7 \cdot 2 sin^{2} (x)

数を乗じる:

7 \cdot 2 = 14

= 7 - 14 sin^{2} (x)

= 7 - 14 sin^{2} (x)

= - 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x)

簡素化

- 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x) : - 21 sin^{2} (x) + 2

- 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x)

類似した元を足す:

- 14 sin^{2} (x) - 7 sin^{2} (x) = - 21 sin^{2} (x)

= - 5 + 7 - 21 sin^{2} (x)

数を足す/引く:

- 5 + 7 = 2

= - 21 sin^{2} (x) + 2

= - 21 sin^{2} (x) + 2

= - 21 sin^{2} (x) + 2

2 - 21 sin^{2} (x) = 0

置換で解く

2 - 21 sin^{2} (x) = 0

仮定:

sin (x) = u

2 - 21 u^{2} = 0

2 - 21 u^{2} = 0 : u = \frac{2}{21}, u = - \frac{2}{21}

2 - 21 u^{2} = 0

2

を右側に移動します

2 - 21 u^{2} = 0

両辺から

2

を引く

2 - 21 u^{2} - 2 = 0 - 2

簡素化

- 21 u^{2} = - 2

- 21 u^{2} = - 2

以下で両辺を割る

- 21

- 21 u^{2} = - 2

以下で両辺を割る

- 21

\frac{- 21 u ^{2}}{- 21} = \frac{- 2}{- 21}

簡素化

u^{2} = \frac{2}{21}

u^{2} = \frac{2}{21}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{2}{21}, u = - \frac{2}{21}

代用を戻す

u = sin (x)

sin (x) = \frac{2}{21}, sin (x) = - \frac{2}{21}

sin (x) = \frac{2}{21}, sin (x) = - \frac{2}{21}

sin (x) = \frac{2}{21} : x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

sin (x) = \frac{2}{21}

三角関数の逆数プロパティを適用する

sin (x) = \frac{2}{21}

以下の一般解

sin (x) = \frac{2}{21}

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

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

sin (x) = - \frac{2}{21} : x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

sin (x) = - \frac{2}{21}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{2}{21}

以下の一般解

sin (x) = - \frac{2}{21}

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

x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn, x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

10進法形式で解を証明する

x = 0.31372 \dots + 2 πn, x = π - 0.31372 \dots + 2 πn, x = - 0.31372 \dots + 2 πn, x = π + 0.31372 \dots + 2 πn

グラフ

人気の例

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

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

(cos(x)*cot(x))/(1-sin(x))=3

\frac{cos ( x ) \cdot cot ( x )}{1 - sin ( x )} = 3

(sin(8))/(30)=(sin(θ))/(120)

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}

114 = sin (x)

cos(θ)=(11.14)/(13)

cos (θ) = \frac{11.14}{13}