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人気のある三角関数 >

3cos^2(x)+3=4,0<= x<2pi

解

3 cos^{2} (x) + 3 = 4, 0 \leq x < 2 π

解

x = 0.95531 \dots, x = 2 π - 0.95531 \dots, x = 2.18627 \dots, x = - 2.18627 \dots + 2 π

+1

度

x = 54.73561 \dots^{\circ}, x = 305.26438 \dots^{\circ}, x = 125.26438 \dots^{\circ}, x = 234.73561 \dots^{\circ}

解答ステップ

3 cos^{2} (x) + 3 = 4, 0 \leq x < 2 π

置換で解く

3 cos^{2} (x) + 3 = 4

仮定:

cos (x) = u

3 u^{2} + 3 = 4

3 u^{2} + 3 = 4 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} + 3 = 4

3

を右側に移動します

3 u^{2} + 3 = 4

両辺から

3

を引く

3 u^{2} + 3 - 3 = 4 - 3

簡素化

3 u^{2} = 1

3 u^{2} = 1

以下で両辺を割る

3

3 u^{2} = 1

以下で両辺を割る

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

簡素化

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3}

x^{2} = f (a)

の場合, 解は

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

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

代用を戻す

u = cos (x)

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

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

cos (x) = \frac{1}{3}, 0 \leq x < 2 π : x = arccos (\frac{1}{3}), x = 2 π - arccos (\frac{1}{3})

cos (x) = \frac{1}{3}, 0 \leq x < 2 π

三角関数の逆数プロパティを適用する

cos (x) = \frac{1}{3}

以下の一般解

cos (x) = \frac{1}{3}

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

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

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

範囲の解答

0 \leq x < 2 π

x = arccos (\frac{1}{3}), x = 2 π - arccos (\frac{1}{3})

cos (x) = - \frac{1}{3}, 0 \leq x < 2 π : x = arccos (- \frac{1}{3}), x = - arccos (- \frac{1}{3}) + 2 π

cos (x) = - \frac{1}{3}, 0 \leq x < 2 π

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

範囲の解答

0 \leq x < 2 π

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 0.95531 \dots, x = 2 π - 0.95531 \dots, x = 2.18627 \dots, x = - 2.18627 \dots + 2 π

グラフ

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