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人気のある三角関数 >

sec^2(x)= 4/3 ,0<= x<= 2pi

解

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

解

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

+1

度

x = 3 0^{\circ}, x = 33 0^{\circ}, x = 15 0^{\circ}, x = 21 0^{\circ}

解答ステップ

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

置換で解く

sec^{2} (x) = \frac{4}{3}

仮定:

sec (x) = u

u^{2} = \frac{4}{3}

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

u^{2} = \frac{4}{3}

x^{2} = f (a)

の場合, 解は

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

u = \frac{4}{3}, u = - \frac{4}{3}

\frac{4}{3} = \frac{2 3}{3}

\frac{4}{3}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

有理化する

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

共役で乗じる

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

- \frac{4}{3} = - \frac{2 3}{3}

- \frac{4}{3}

簡素化

\frac{4}{3} : \frac{2}{3}

\frac{4}{3}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{3}

= - \frac{2}{3}

有理化する

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

共役で乗じる

\frac{3}{3}

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

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

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

代用を戻す

u = sec (x)

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

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

sec (x) = \frac{2 3}{3}, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{11 π}{6}

sec (x) = \frac{2 3}{3}, 0 \leq x \leq 2 π

以下の一般解

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

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}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{11 π}{6}

sec (x) = - \frac{2 3}{3}, 0 \leq x \leq 2 π : x = \frac{5 π}{6}, x = \frac{7 π}{6}

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

以下の一般解

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

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{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{5 π}{6}, x = \frac{7 π}{6}

すべての解を組み合わせる

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

グラフ

人気の例

sqrt(3)tan(3θ)-1=0

3 tan (3 θ) - 1 = 0

2 tan (x) = sec (x)

cos (x) = 2 π

sin(6x)+sin(2x)=0

sin (6 x) + sin (2 x) = 0

cos (a) = - \frac{1}{2}