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)= 1/2

解

sin^{22} (x) = \frac{1}{2}

解

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

+1

度

x = 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 104.30724 \dots^{\circ} + 36 0^{\circ} n, x = - 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 255.69275 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{22} (x) = \frac{1}{2}

置換で解く

sin^{22} (x) = \frac{1}{2}

仮定:

sin (x) = u

u^{22} = \frac{1}{2}

u^{22} = \frac{1}{2} : u = 22 \frac{1}{2}, u = - 22 \frac{1}{2}

u^{22} = \frac{1}{2}

x^{n} = f (a)

の場合, n は偶数, 解は

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

u = 22 \frac{1}{2}, u = - 22 \frac{1}{2}

代用を戻す

u = sin (x)

sin (x) = 22 \frac{1}{2}, sin (x) = - 22 \frac{1}{2}

sin (x) = 22 \frac{1}{2}, sin (x) = - 22 \frac{1}{2}

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

sin (x) = 22 \frac{1}{2}

三角関数の逆数プロパティを適用する

sin (x) = 22 \frac{1}{2}

以下の一般解

sin (x) = 22 \frac{1}{2}

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

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

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

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

sin (x) = - 22 \frac{1}{2}

三角関数の逆数プロパティを適用する

sin (x) = - 22 \frac{1}{2}

以下の一般解

sin (x) = - 22 \frac{1}{2}

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

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

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

グラフ

人気の例

cos^5(x)=cos(x)

cos^{5} (x) = cos (x)

tan(x)=((1.8)/(3.6))

tan (x) = (\frac{1.8}{3.6})

sec (x + 3 0^{\circ}) = 2

solvefor y,arccos(y/2)=5log_{10}(x/5)

so l v e f or y, arccos (\frac{y}{2}) = 5 lo g_{10} (\frac{x}{5})

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

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