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人気のある三角関数 >

5sin^2(x)-1=0

解

5 sin^{2} (x) - 1 = 0

解

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

+1

度

x = 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 153.43494 \dots^{\circ} + 36 0^{\circ} n, x = - 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 206.56505 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

5 sin^{2} (x) - 1 = 0

置換で解く

5 sin^{2} (x) - 1 = 0

仮定:

sin (x) = u

5 u^{2} - 1 = 0

5 u^{2} - 1 = 0 : u = \frac{1}{5}, u = - \frac{1}{5}

5 u^{2} - 1 = 0

1

を右側に移動します

5 u^{2} - 1 = 0

両辺に

1

を足す

5 u^{2} - 1 + 1 = 0 + 1

簡素化

5 u^{2} = 1

5 u^{2} = 1

以下で両辺を割る

5

5 u^{2} = 1

以下で両辺を割る

5

\frac{5 u ^{2}}{5} = \frac{1}{5}

簡素化

u^{2} = \frac{1}{5}

u^{2} = \frac{1}{5}

x^{2} = f (a)

の場合, 解は

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

u = \frac{1}{5}, u = - \frac{1}{5}

代用を戻す

u = sin (x)

sin (x) = \frac{1}{5}, sin (x) = - \frac{1}{5}

sin (x) = \frac{1}{5}, sin (x) = - \frac{1}{5}

sin (x) = \frac{1}{5} : x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

sin (x) = \frac{1}{5}

三角関数の逆数プロパティを適用する

sin (x) = \frac{1}{5}

以下の一般解

sin (x) = \frac{1}{5}

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

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

sin (x) = - \frac{1}{5} : x = arcsin (- \frac{1}{5}) + 2 πn, x = π + arcsin (\frac{1}{5}) + 2 πn

sin (x) = - \frac{1}{5}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{1}{5}

以下の一般解

sin (x) = - \frac{1}{5}

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

x = arcsin (- \frac{1}{5}) + 2 πn, x = π + arcsin (\frac{1}{5}) + 2 πn

x = arcsin (- \frac{1}{5}) + 2 πn, x = π + arcsin (\frac{1}{5}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn, x = arcsin (- \frac{1}{5}) + 2 πn, x = π + arcsin (\frac{1}{5}) + 2 πn

10進法形式で解を証明する

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

グラフ

人気の例

sin^2(θ)=sin(θ)+1-sin^2(θ)

sin^{2} (θ) = sin (θ) + 1 - sin^{2} (θ)

sin (x) = 0.75

(cot(θ)-1)(csc(θ)+1)=0

(cot (θ) - 1) (csc (θ) + 1) = 0

tan (θ) = - \frac{2}{3}

cot^2(x)=csc(x)-1

cot^{2} (x) = csc (x) - 1