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人気のある三角関数 >

(cot^2(x))/2 =3

解

\frac{cot ^{2} ( x )}{2} = 3

解

x = 0.38759 \dots + πn, x = 2.75399 \dots + πn

+1

度

x = 22.20765 \dots^{\circ} + 18 0^{\circ} n, x = 157.79234 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

\frac{cot ^{2} ( x )}{2} = 3

置換で解く

\frac{cot ^{2} ( x )}{2} = 3

仮定:

cot (x) = u

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

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

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

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

簡素化

u^{2} = 6

u^{2} = 6

x^{2} = f (a)

の場合, 解は

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

u = 6, u = - 6

代用を戻す

u = cot (x)

cot (x) = 6, cot (x) = - 6

cot (x) = 6, cot (x) = - 6

cot (x) = 6 : x = arccot (6) + πn

cot (x) = 6

三角関数の逆数プロパティを適用する

cot (x) = 6

以下の一般解

cot (x) = 6

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (6) + πn

x = arccot (6) + πn

cot (x) = - 6 : x = arccot (- 6) + πn

cot (x) = - 6

三角関数の逆数プロパティを適用する

cot (x) = - 6

以下の一般解

cot (x) = - 6

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- 6) + πn

x = arccot (- 6) + πn

すべての解を組み合わせる

x = arccot (6) + πn, x = arccot (- 6) + πn

10進法形式で解を証明する

x = 0.38759 \dots + πn, x = 2.75399 \dots + πn

グラフ

人気の例

sin (x - 3 0^{\circ}) = 0.7

<= sqrt(3)*cos(x)-sin(x)=0

\leq 3 \cdot cos (x) - sin (x) = 0

tan^2(x)+sec^2(x)=3

tan^{2} (x) + sec^{2} (x) = 3

4sin^2(x)-6cos^2(x)=0

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

sin(60-a)=0.598

sin (6 0^{\circ} - a) = 0.598