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人気のある三角関数 >

3cos^2(x)-3=sin(x)

解

3 cos^{2} (x) - 3 = sin (x)

解

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

+1

度

x = - 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 199.47122 \dots^{\circ} + 36 0^{\circ} n, x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

3 cos^{2} (x) - 3 = sin (x)

両辺から

sin (x)

を引く

3 cos^{2} (x) - 3 - sin (x) = 0

三角関数の公式を使用して書き換える

- 3 - sin (x) + 3 cos^{2} (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)

= - 3 - sin (x) + 3 (1 - sin^{2} (x))

簡素化

- 3 - sin (x) + 3 (1 - sin^{2} (x)) : - 3 sin^{2} (x) - sin (x)

- 3 - sin (x) + 3 (1 - sin^{2} (x))

拡張

3 (1 - sin^{2} (x)) : 3 - 3 sin^{2} (x)

3 (1 - sin^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 3, b = 1, c = sin^{2} (x)

= 3 \cdot 1 - 3 sin^{2} (x)

数を乗じる:

3 \cdot 1 = 3

= 3 - 3 sin^{2} (x)

= - 3 - sin (x) + 3 - 3 sin^{2} (x)

簡素化

- 3 - sin (x) + 3 - 3 sin^{2} (x) : - 3 sin^{2} (x) - sin (x)

- 3 - sin (x) + 3 - 3 sin^{2} (x)

条件のようなグループ

= - sin (x) - 3 sin^{2} (x) - 3 + 3

- 3 + 3 = 0

= - 3 sin^{2} (x) - sin (x)

= - 3 sin^{2} (x) - sin (x)

= - 3 sin^{2} (x) - sin (x)

- sin (x) - 3 sin^{2} (x) = 0

置換で解く

- sin (x) - 3 sin^{2} (x) = 0

仮定:

sin (x) = u

- u - 3 u^{2} = 0

- u - 3 u^{2} = 0 : u = - \frac{1}{3}, u = 0

- u - 3 u^{2} = 0

標準的な形式で書く

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

- 3 u^{2} - u = 0

解くとthe二次式

- 3 u^{2} - u = 0

二次Equationの公式:

次の場合:

a = - 3, b = - 1, c = 0

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 3 ) \cdot 0}{2 ( - 3 )}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 3 ) \cdot 0}{2 ( - 3 )}

(- 1)^{2} - 4 (- 3) \cdot 0 = 1

(- 1)^{2} - 4 (- 3) \cdot 0

規則を適用

- (- a) = a

= (- 1)^{2} + 4 \cdot 3 \cdot 0

(- 1)^{2} = 1

(- 1)^{2}

指数の規則を適用する:

n

が偶数であれば

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

(- 1)^{2} = 1^{2}

= 1^{2}

規則を適用

1^{a} = 1

= 1

4 \cdot 3 \cdot 0 = 0

4 \cdot 3 \cdot 0

規則を適用

0 \cdot a = 0

= 0

= 1 + 0

数を足す:

1 + 0 = 1

= 1

規則を適用

1 = 1

= 1

u_{1, 2} = \frac{- ( - 1 ) \pm 1}{2 ( - 3 )}

解を分離する

u_{1} = \frac{- ( - 1 ) + 1}{2 ( - 3 )}, u_{2} = \frac{- ( - 1 ) - 1}{2 ( - 3 )}

u = \frac{- ( - 1 ) + 1}{2 ( - 3 )} : - \frac{1}{3}

\frac{- ( - 1 ) + 1}{2 ( - 3 )}

括弧を削除する:

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

= \frac{1 + 1}{- 2 \cdot 3}

数を足す:

1 + 1 = 2

= \frac{2}{- 2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{2}{- 6}

分数の規則を適用する:

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

= - \frac{2}{6}

共通因数を約分する:

2

= - \frac{1}{3}

u = \frac{- ( - 1 ) - 1}{2 ( - 3 )} : 0

\frac{- ( - 1 ) - 1}{2 ( - 3 )}

括弧を削除する:

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

= \frac{1 - 1}{- 2 \cdot 3}

数を引く:

1 - 1 = 0

= \frac{0}{- 2 \cdot 3}

数を乗じる:

2 \cdot 3 = 6

= \frac{0}{- 6}

分数の規則を適用する:

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

= - \frac{0}{6}

規則を適用

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

= - 0

= 0

二次equationの解:

u = - \frac{1}{3}, u = 0

代用を戻す

u = sin (x)

sin (x) = - \frac{1}{3}, sin (x) = 0

sin (x) = - \frac{1}{3}, sin (x) = 0

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

グラフ

人気の例

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

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

tan(x-pi/2)= 1/(sqrt(3))

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2sin^2(x)+cos(x)+1=0

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