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人気のある三角関数 >

6cos^2(x)-4=0

解

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

解

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

+1

度

x = 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 324.73561 \dots^{\circ} + 36 0^{\circ} n, x = 144.73561 \dots^{\circ} + 36 0^{\circ} n, x = - 144.73561 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

cos (x) = u

6 u^{2} - 4 = 0

6 u^{2} - 4 = 0 : u = \frac{2}{3}, u = - \frac{2}{3}

6 u^{2} - 4 = 0

4

を右側に移動します

6 u^{2} - 4 = 0

両辺に

4

を足す

6 u^{2} - 4 + 4 = 0 + 4

簡素化

6 u^{2} = 4

6 u^{2} = 4

以下で両辺を割る

6

6 u^{2} = 4

以下で両辺を割る

6

\frac{6 u ^{2}}{6} = \frac{4}{6}

簡素化

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

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

x^{2} = f (a)

の場合, 解は

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

u = \frac{2}{3}, u = - \frac{2}{3}

代用を戻す

u = cos (x)

cos (x) = \frac{2}{3}, cos (x) = - \frac{2}{3}

cos (x) = \frac{2}{3}, cos (x) = - \frac{2}{3}

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

cos (x) = \frac{2}{3}

三角関数の逆数プロパティを適用する

cos (x) = \frac{2}{3}

以下の一般解

cos (x) = \frac{2}{3}

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

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

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

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

cos (x) = - \frac{2}{3}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{2}{3}

以下の一般解

cos (x) = - \frac{2}{3}

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

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

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

グラフ

人気の例

csc (x) = 3.5

sin(x)=0,sin(x)=0

sin (x) = 0, sin (x) = 0

cos(x)=-7/9 , pi/2 <x<pi

cos (x) = - \frac{7}{9}, \frac{π}{2} < x < π

solvefor y,x+arctan(y/x)=0

so l v e f or y, x + arctan (\frac{y}{x}) = 0

sin(45+2α)=(sqrt(3))/2

sin (45 + 2 α) = \frac{3}{2}