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 >

sin^{22}(x)= 1/4

解

sin^{22} (x) = \frac{1}{4}

解

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

+1

度

x = 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 110.12721 \dots^{\circ} + 36 0^{\circ} n, x = - 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 249.87278 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{22} (x) = \frac{1}{4}

置換で解く

sin^{22} (x) = \frac{1}{4}

仮定:

sin (x) = u

u^{22} = \frac{1}{4}

u^{22} = \frac{1}{4} : u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

u^{22} = \frac{1}{4}

x^{n} = f (a)

の場合, n は偶数, 解は

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

u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

代用を戻す

u = sin (x)

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4} : x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = 22 \frac{1}{4}

三角関数の逆数プロパティを適用する

sin (x) = 22 \frac{1}{4}

以下の一般解

sin (x) = 22 \frac{1}{4}

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

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4} : x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4}

三角関数の逆数プロパティを適用する

sin (x) = - 22 \frac{1}{4}

以下の一般解

sin (x) = - 22 \frac{1}{4}

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

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

すべての解を組み合わせる

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn, x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

10進法形式で解を証明する

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

グラフ

人気の例

3sin(2x)-cos(x)=0

3 sin (2 x) - cos (x) = 0

2cos^2(x)+tan^2(x)=2

2 cos^{2} (x) + tan^{2} (x) = 2

sin^3(o)=4sin(o)sin^2(o)sin^4(o)

sin^{3} (o) = 4 sin (o) sin^{2} (o) sin^{4} (o)

cos^{2} (x) = - 4

8sin^4(x)-6sin^2(x)+1=0

8 sin^{4} (x) - 6 sin^{2} (x) + 1 = 0