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人気のある三角関数 >

sec^2(x)-2=0,0<= x<= 2pi

解

sec^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

解

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

+1

度

x = 4 5^{\circ}, x = 31 5^{\circ}, x = 13 5^{\circ}, x = 22 5^{\circ}

解答ステップ

sec^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

置換で解く

sec^{2} (x) - 2 = 0

仮定:

sec (x) = u

u^{2} - 2 = 0

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

u^{2} - 2 = 0

2

を右側に移動します

u^{2} - 2 = 0

両辺に

2

を足す

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

簡素化

u^{2} = 2

u^{2} = 2

x^{2} = f (a)

の場合, 解は

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

u = 2, u = - 2

代用を戻す

u = sec (x)

sec (x) = 2, sec (x) = - 2

sec (x) = 2, sec (x) = - 2

sec (x) = 2, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{7 π}{4}

sec (x) = 2, 0 \leq x \leq 2 π

以下の一般解

sec (x) = 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{7 π}{4}

sec (x) = - 2, 0 \leq x \leq 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

sec (x) = - 2, 0 \leq x \leq 2 π

以下の一般解

sec (x) = - 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{3 π}{4}, x = \frac{5 π}{4}

すべての解を組み合わせる

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

グラフ

人気の例

\frac{1}{2} = sin (2 θ)

sin(2x)+sin(x)=sin(3x)

sin (2 x) + sin (x) = sin (3 x)

sin(2x)=2sqrt(3)sin^2(x)

sin (2 x) = 23 sin^{2} (x)

cosh (x) = 5

cosh (x) = 7