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人気のある三角関数 >

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

解

2 cos^{2} (x) + 3 sin^{2} (x) = 2

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

2 cos^{2} (x) + 3 sin^{2} (x) = 2

両辺から

2

を引く

2 cos^{2} (x) + 3 sin^{2} (x) - 2 = 0

三角関数の公式を使用して書き換える

- 2 + 2 cos^{2} (x) + 3 sin^{2} (x)

ピタゴラスの公式を使用する:

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

cos^{2} (x) = 1 - sin^{2} (x)

= - 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

簡素化

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x) : sin^{2} (x)

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

拡張

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

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

分配法則を適用する:

a (b - c) = ab - a c

a = 2, b = 1, c = sin^{2} (x)

= 2 \cdot 1 - 2 sin^{2} (x)

数を乗じる:

2 \cdot 1 = 2

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

= - 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x)

簡素化

- 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x) : sin^{2} (x)

- 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x)

類似した元を足す:

- 2 sin^{2} (x) + 3 sin^{2} (x) = sin^{2} (x)

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

- 2 + 2 = 0

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

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

グラフ

人気の例

42 - 25 cos (x) = 31

2sec^2(x)=5tan(x)

2 sec^{2} (x) = 5 tan (x)

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