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人気のある三角関数 >

sin^2(x)=sin^2(x)sec(x)

解

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

解

x = 2 πn, x = π + 2 πn

+1

度

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

解答ステップ

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

両辺から

sin^{2} (x) sec (x)

を引く

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

因数

sin^{2} (x) - sin^{2} (x) sec (x) : - sin^{2} (x) (sec (x) - 1)

sin^{2} (x) - sin^{2} (x) sec (x)

共通項をくくり出す

- sin^{2} (x)

= - sin^{2} (x) (- 1 + sec (x))

- sin^{2} (x) (sec (x) - 1) = 0

各部分を別個に解く

sin^{2} (x) = 0 or sec (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{2} (x) = 0

規則を適用

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

以下の一般解

sin (x) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0

1

を右側に移動します

sec (x) - 1 = 0

両辺に

1

を足す

sec (x) - 1 + 1 = 0 + 1

簡素化

sec (x) = 1

sec (x) = 1

以下の一般解

sec (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

グラフ

人気の例

sin(x)=(4.2)/(9.5)

sin (x) = \frac{4.2}{9.5}

cos(x)=(4.6)/(8.6)

cos (x) = \frac{4.6}{8.6}

5tan(x)+5tan^2(x)=0

5 tan (x) + 5 tan^{2} (x) = 0

8sec^2(x)-8sec(x)=16

8 sec^{2} (x) - 8 sec (x) = 16

50=36sin((2pi)/(365)(t-101))+14

50 = 36 sin (\frac{2 π}{365} (t - 101)) + 14