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人気のある三角関数 >

cos^3(x)=-cos^2(x)

解

cos^{3} (x) = - cos^{2} (x)

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{3} (x) = - cos^{2} (x)

置換で解く

cos^{3} (x) = - cos^{2} (x)

仮定:

cos (x) = u

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

u^{3} = - u^{2} : u = 0, u = - 1

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

u^{2}

を左側に移動します

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

両辺に

u^{2}

を足す

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

簡素化

u^{3} + u^{2} = 0

u^{3} + u^{2} = 0

因数

u^{3} + u^{2} : u^{2} (u + 1)

u^{3} + u^{2}

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

u^{3} = u u^{2}

= u u^{2} + u^{2}

共通項をくくり出す

u^{2}

= u^{2} (u + 1)

u^{2} (u + 1) = 0

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

u = 0 or u + 1 = 0

解く

u + 1 = 0 : u = - 1

u + 1 = 0

1

を右側に移動します

u + 1 = 0

両辺から

1

を引く

u + 1 - 1 = 0 - 1

簡素化

u = - 1

u = - 1

解答は

u = 0, u = - 1

代用を戻す

u = cos (x)

cos (x) = 0, cos (x) = - 1

cos (x) = 0, cos (x) = - 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

cos (x)

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

以下の一般解

cos (x) = - 1

cos (x)

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = π + 2 πn

x = π + 2 πn

すべての解を組み合わせる

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = π + 2 πn

グラフ

人気の例

sqrt(3)sec(2x)+2=0

3 sec (2 x) + 2 = 0

e^{t a n (x)} - 2 = 0

cos(x)+cos^2(x)-sin^2(x)=0

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

solvefor x,2sin(x)+csc(x)=0

so l v e f or x, 2 sin (x) + csc (x) = 0

sin(2x+pi/6)=-1/2

sin (2 x + \frac{π}{6}) = - \frac{1}{2}