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人気のある三角関数 >

4-8cos^2(x)=0

解

4 - 8 cos^{2} (x) = 0

解

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

+1

度

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = - 13 5^{\circ} + 36 0^{\circ} n

解答ステップ

4 - 8 cos^{2} (x) = 0

置換で解く

4 - 8 cos^{2} (x) = 0

仮定:

cos (x) = u

4 - 8 u^{2} = 0

4 - 8 u^{2} = 0 : u = \frac{1}{2}, u = - \frac{1}{2}

4 - 8 u^{2} = 0

4

を右側に移動します

4 - 8 u^{2} = 0

両辺から

4

を引く

4 - 8 u^{2} - 4 = 0 - 4

簡素化

- 8 u^{2} = - 4

- 8 u^{2} = - 4

以下で両辺を割る

- 8

- 8 u^{2} = - 4

以下で両辺を割る

- 8

\frac{- 8 u ^{2}}{- 8} = \frac{- 4}{- 8}

簡素化

\frac{- 8 u ^{2}}{- 8} = \frac{- 4}{- 8}

簡素化

\frac{- 8 u ^{2}}{- 8} : u^{2}

\frac{- 8 u ^{2}}{- 8}

分数の規則を適用する:

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

= \frac{8 u ^{2}}{8}

数を割る:

\frac{8}{8} = 1

= u^{2}

簡素化

\frac{- 4}{- 8} : \frac{1}{2}

\frac{- 4}{- 8}

分数の規則を適用する:

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

= \frac{4}{8}

共通因数を約分する:

4

= \frac{1}{2}

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

x^{2} = f (a)

の場合, 解は

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

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

代用を戻す

u = cos (x)

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

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

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

cos (x) = \frac{1}{2}

三角関数の逆数プロパティを適用する

cos (x) = \frac{1}{2}

以下の一般解

cos (x) = \frac{1}{2}

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

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

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

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

グラフ

人気の例

cos^2(x)-4cos(x)-1=0

cos^{2} (x) - 4 cos (x) - 1 = 0

- 9 sin (3 x) = 0

cos(4x)-7cos(2x)=8

cos (4 x) - 7 cos (2 x) = 8

6tan(B)+sqrt(14)=0

6 tan (B) + 14 = 0

-4tan^2(θ)-4tan(θ)-9=8tan(θ)-4

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4