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人気のある三角関数 >

sin^2(x)= 1/36

解

sin^{2} (x) = \frac{1}{36}

解

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

+1

度

x = 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 170.40593 \dots^{\circ} + 36 0^{\circ} n, x = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 189.59406 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) = \frac{1}{36}

置換で解く

sin^{2} (x) = \frac{1}{36}

仮定:

sin (x) = u

u^{2} = \frac{1}{36}

u^{2} = \frac{1}{36} : u = \frac{1}{6}, u = - \frac{1}{6}

u^{2} = \frac{1}{36}

x^{2} = f (a)

の場合, 解は

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

u = \frac{1}{36}, u = - \frac{1}{36}

\frac{1}{36} = \frac{1}{6}

\frac{1}{36}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

数を因数に分解する:

36 = 6^{2}

= 6^{2}

累乗根の規則を適用する:

n a^{n} = a

6^{2} = 6

= 6

= \frac{1}{6}

規則を適用

1 = 1

= \frac{1}{6}

- \frac{1}{36} = - \frac{1}{6}

- \frac{1}{36}

簡素化

\frac{1}{36} : \frac{1}{6}

\frac{1}{36}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

数を因数に分解する:

36 = 6^{2}

= 6^{2}

累乗根の規則を適用する:

n a^{n} = a

6^{2} = 6

= 6

= \frac{1}{6}

= - \frac{1}{6}

規則を適用

1 = 1

= - \frac{1}{6}

u = \frac{1}{6}, u = - \frac{1}{6}

代用を戻す

u = sin (x)

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6} : x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = \frac{1}{6}

三角関数の逆数プロパティを適用する

sin (x) = \frac{1}{6}

以下の一般解

sin (x) = \frac{1}{6}

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

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6} : x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{1}{6}

以下の一般解

sin (x) = - \frac{1}{6}

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

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn, x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

10進法形式で解を証明する

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

グラフ

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