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人気のある三角関数 >

cot^2(x)+1=2

解

cot^{2} (x) + 1 = 2

解

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

+1

度

x = 4 5^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

解答ステップ

cot^{2} (x) + 1 = 2

置換で解く

cot^{2} (x) + 1 = 2

仮定:

cot (x) = u

u^{2} + 1 = 2

u^{2} + 1 = 2 : u = 1, u = - 1

u^{2} + 1 = 2

1

を右側に移動します

u^{2} + 1 = 2

両辺から

1

を引く

u^{2} + 1 - 1 = 2 - 1

簡素化

u^{2} = 1

u^{2} = 1

x^{2} = f (a)

の場合, 解は

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

u = 1, u = - 1

1 = 1

1

規則を適用

1 = 1

= 1

- 1 = - 1

- 1

規則を適用

1 = 1

= - 1

u = 1, u = - 1

代用を戻す

u = cot (x)

cot (x) = 1, cot (x) = - 1

cot (x) = 1, cot (x) = - 1

cot (x) = 1 : x = \frac{π}{4} + πn

cot (x) = 1

以下の一般解

cot (x) = 1

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

cot (x) = - 1 : x = \frac{3 π}{4} + πn

cot (x) = - 1

以下の一般解

cot (x) = - 1

cot (x)

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

すべての解を組み合わせる

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

グラフ

人気の例

sin(x)= 1/3 ,sec(y)=(25)/(24,cos(x+y))

sin (x) = \frac{1}{3}, sec (y) = \frac{25}{24 , cos ( x + y )}

2 = 2 - π cos (t)

solvefor a,45=arctanh(a/b)

so l v e f or a, 45 = arctanh (\frac{a}{b})

solvefor x,sec(x)=3

so l v e f or x, sec (x) = 3

cot(θ-30)= 1/(sqrt(3))

cot (θ - 3 0^{\circ}) = \frac{1}{3}