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人気のある三角関数 >

2sec^2(x)-5sec(x)+2=0,0<= x<= 360

解

2 sec^{2} (x) - 5 sec (x) + 2 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

解

x = 6 0^{\circ}, x = 30 0^{\circ}

+1

ラジアン

x = \frac{π}{3}, x = \frac{5 π}{3}

解答ステップ

2 sec^{2} (x) - 5 sec (x) + 2 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

置換で解く

2 sec^{2} (x) - 5 sec (x) + 2 = 0

仮定:

sec (x) = u

2 u^{2} - 5 u + 2 = 0

2 u^{2} - 5 u + 2 = 0 : u = 2, u = \frac{1}{2}

2 u^{2} - 5 u + 2 = 0

解くとthe二次式

2 u^{2} - 5 u + 2 = 0

二次Equationの公式:

次の場合:

a = 2, b = - 5, c = 2

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 \cdot 2}{2 \cdot 2}

u_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 \cdot 2}{2 \cdot 2}

(- 5)^{2} - 4 \cdot 2 \cdot 2 = 3

(- 5)^{2} - 4 \cdot 2 \cdot 2

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- 5)^{2} = 5^{2}

= 5^{2} - 4 \cdot 2 \cdot 2

数を乗じる:

4 \cdot 2 \cdot 2 = 16

= 5^{2} - 16

5^{2} = 25

= 25 - 16

数を引く:

25 - 16 = 9

= 9

数を因数に分解する:

9 = 3^{2}

= 3^{2}

累乗根の規則を適用する:

n a^{n} = a

3^{2} = 3

= 3

u_{1, 2} = \frac{- ( - 5 ) \pm 3}{2 \cdot 2}

解を分離する

u_{1} = \frac{- ( - 5 ) + 3}{2 \cdot 2}, u_{2} = \frac{- ( - 5 ) - 3}{2 \cdot 2}

u = \frac{- ( - 5 ) + 3}{2 \cdot 2} : 2

\frac{- ( - 5 ) + 3}{2 \cdot 2}

規則を適用

- (- a) = a

= \frac{5 + 3}{2 \cdot 2}

数を足す:

5 + 3 = 8

= \frac{8}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{8}{4}

数を割る:

\frac{8}{4} = 2

= 2

u = \frac{- ( - 5 ) - 3}{2 \cdot 2} : \frac{1}{2}

\frac{- ( - 5 ) - 3}{2 \cdot 2}

規則を適用

- (- a) = a

= \frac{5 - 3}{2 \cdot 2}

数を引く:

5 - 3 = 2

= \frac{2}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{2}{4}

共通因数を約分する:

2

= \frac{1}{2}

二次equationの解:

u = 2, u = \frac{1}{2}

代用を戻す

u = sec (x)

sec (x) = 2, sec (x) = \frac{1}{2}

sec (x) = 2, sec (x) = \frac{1}{2}

sec (x) = 2, 0 \leq x \leq 36 0^{\circ} : x = 6 0^{\circ}, x = 30 0^{\circ}

sec (x) = 2, 0 \leq x \leq 36 0^{\circ}

以下の一般解

sec (x) = 2

sec (x)

36 0^{\circ} n

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 = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq x \leq 36 0^{\circ}

x = 6 0^{\circ}, x = 30 0^{\circ}

sec (x) = \frac{1}{2}, 0 \leq x \leq 36 0^{\circ} :

解なし

sec (x) = \frac{1}{2}, 0 \leq x \leq 36 0^{\circ}

sec (x) \leq - 1 or sec (x) \geq 1

解なし

すべての解を組み合わせる

x = 6 0^{\circ}, x = 30 0^{\circ}

グラフ

人気の例

2sin(5x)+sqrt(3)=0,0<= x<= 2pi

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

sin(2θ)=-24/25

sin (2 θ) = - \frac{24}{25}

sin(4x)+cos(4x)=1

sin (4 x) + cos (4 x) = 1

cos (A) = 0.7865

sin(x)=cos(2x+51)

sin (x) = cos (2 x + 5 1^{\circ})