ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

2sin^2(x)-sqrt(2)=0

解

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

解

x = 0.99893 \dots + 2 πn, x = π - 0.99893 \dots + 2 πn, x = - 0.99893 \dots + 2 πn, x = π + 0.99893 \dots + 2 πn

+1

度

x = 57.23490 \dots^{\circ} + 36 0^{\circ} n, x = 122.76509 \dots^{\circ} + 36 0^{\circ} n, x = - 57.23490 \dots^{\circ} + 36 0^{\circ} n, x = 237.23490 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

sin (x) = u

2 u^{2} - 2 = 0

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

2 u^{2} - 2 = 0

2

を右側に移動します

2 u^{2} - 2 = 0

両辺に

2

を足す

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

簡素化

2 u^{2} = 2

2 u^{2} = 2

以下で両辺を割る

2

2 u^{2} = 2

以下で両辺を割る

2

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

簡素化

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

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

x^{2} = f (a)

の場合, 解は

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

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

代用を戻す

u = sin (x)

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

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

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 0.99893 \dots + 2 πn, x = π - 0.99893 \dots + 2 πn, x = - 0.99893 \dots + 2 πn, x = π + 0.99893 \dots + 2 πn

グラフ

人気の例

solvefor x,z=sin(5x)y^3

so l v e f or x, z = sin (5 x) y^{3}

8tan^2(θ)-1=3tan(θ)+4

8 tan^{2} (θ) - 1 = 3 tan (θ) + 4

sqrt(2)csc^2(x)+csc(x)-sqrt(2)=0

2 csc^{2} (x) + csc (x) - 2 = 0

2 sin (A) - 1 = 0

cos(5θ)=cos(3θ)

cos (5 θ) = cos (3 θ)