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人気のある三角関数 >

-3sin^2(x)+2=0

解

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

解

x = 0.95531 \dots + 2 πn, x = π - 0.95531 \dots + 2 πn, x = - 0.95531 \dots + 2 πn, x = π + 0.95531 \dots + 2 πn

+1

度

x = 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 125.26438 \dots^{\circ} + 36 0^{\circ} n, x = - 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 234.73561 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

sin (x) = u

- 3 u^{2} + 2 = 0

- 3 u^{2} + 2 = 0 : u = \frac{2}{3}, u = - \frac{2}{3}

- 3 u^{2} + 2 = 0

2

を右側に移動します

- 3 u^{2} + 2 = 0

両辺から

2

を引く

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

簡素化

- 3 u^{2} = - 2

- 3 u^{2} = - 2

以下で両辺を割る

- 3

- 3 u^{2} = - 2

以下で両辺を割る

- 3

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

簡素化

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

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

x^{2} = f (a)

の場合, 解は

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

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

代用を戻す

u = sin (x)

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

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

sin (x) = \frac{2}{3} : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

sin (x) = - \frac{2}{3} : x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn, x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

10進法形式で解を証明する

x = 0.95531 \dots + 2 πn, x = π - 0.95531 \dots + 2 πn, x = - 0.95531 \dots + 2 πn, x = π + 0.95531 \dots + 2 πn

グラフ

人気の例

16sin(3x)cos(x)+8sqrt(3)sin(3x)-2cos(x)-sqrt(3)=0

16 sin (3 x) cos (x) + 83 sin (3 x) - 2 cos (x) - 3 = 0

tan (C) = 2.56

cos (3 y) = 0

tan(x)=(0.33)/(0.44)

tan (x) = \frac{0.33}{0.44}

tan (2 x) = - 0.5