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人気のある三角関数 >

7sin^2(x)-1=0

解

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

解

x = 0.38759 \dots + 2 πn, x = π - 0.38759 \dots + 2 πn, x = - 0.38759 \dots + 2 πn, x = π + 0.38759 \dots + 2 πn

+1

度

x = 22.20765 \dots^{\circ} + 36 0^{\circ} n, x = 157.79234 \dots^{\circ} + 36 0^{\circ} n, x = - 22.20765 \dots^{\circ} + 36 0^{\circ} n, x = 202.20765 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

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

置換で解く

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

仮定:

sin (x) = u

7 u^{2} - 1 = 0

7 u^{2} - 1 = 0 : u = \frac{1}{7}, u = - \frac{1}{7}

7 u^{2} - 1 = 0

1

を右側に移動します

7 u^{2} - 1 = 0

両辺に

1

を足す

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

簡素化

7 u^{2} = 1

7 u^{2} = 1

以下で両辺を割る

7

7 u^{2} = 1

以下で両辺を割る

7

\frac{7 u ^{2}}{7} = \frac{1}{7}

簡素化

u^{2} = \frac{1}{7}

u^{2} = \frac{1}{7}

x^{2} = f (a)

の場合, 解は

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

u = \frac{1}{7}, u = - \frac{1}{7}

代用を戻す

u = sin (x)

sin (x) = \frac{1}{7}, sin (x) = - \frac{1}{7}

sin (x) = \frac{1}{7}, sin (x) = - \frac{1}{7}

sin (x) = \frac{1}{7} : x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn

sin (x) = \frac{1}{7}

三角関数の逆数プロパティを適用する

sin (x) = \frac{1}{7}

以下の一般解

sin (x) = \frac{1}{7}

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

x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn

x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn

sin (x) = - \frac{1}{7} : x = arcsin (- \frac{1}{7}) + 2 πn, x = π + arcsin (\frac{1}{7}) + 2 πn

sin (x) = - \frac{1}{7}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{1}{7}

以下の一般解

sin (x) = - \frac{1}{7}

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

x = arcsin (- \frac{1}{7}) + 2 πn, x = π + arcsin (\frac{1}{7}) + 2 πn

x = arcsin (- \frac{1}{7}) + 2 πn, x = π + arcsin (\frac{1}{7}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{1}{7}) + 2 πn, x = π - arcsin (\frac{1}{7}) + 2 πn, x = arcsin (- \frac{1}{7}) + 2 πn, x = π + arcsin (\frac{1}{7}) + 2 πn

10進法形式で解を証明する

x = 0.38759 \dots + 2 πn, x = π - 0.38759 \dots + 2 πn, x = - 0.38759 \dots + 2 πn, x = π + 0.38759 \dots + 2 πn

グラフ

人気の例

sec^2(x)=tan(x)

sec^{2} (x) = tan (x)

solvefor x,cos(x)=-1/2

so l v e f or x, cos (x) = - \frac{1}{2}

solvefor x,θ=arctan(y/x)

so l v e f or x, θ = arctan (\frac{y}{x})

cos(x)tan(x)=10tan(x)

cos (x) tan (x) = 10 tan (x)

cos (2 x) = \frac{3}{5}