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人気のある三角関数 >

sin^2(x)+cos^2(2/5)=1

解

sin^{2} (x) + cos^{2} (\frac{2}{5}) = 1

解

x = 0.4 + 2 πn, x = π - 0.4 + 2 πn, x = - 0.4 + 2 πn, x = π + 0.4 + 2 πn

+1

度

x = 22.91831 \dots^{\circ} + 36 0^{\circ} n, x = 157.08168 \dots^{\circ} + 36 0^{\circ} n, x = - 22.91831 \dots^{\circ} + 36 0^{\circ} n, x = 202.91831 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) + cos^{2} (\frac{2}{5}) = 1

置換で解く

sin^{2} (x) + cos^{2} (\frac{2}{5}) = 1

仮定:

sin (x) = u

u^{2} + cos^{2} (\frac{2}{5}) = 1

u^{2} + cos^{2} (\frac{2}{5}) = 1 : u = 1 - cos^{2} (\frac{2}{5}), u = - 1 - cos^{2} (\frac{2}{5})

u^{2} + cos^{2} (\frac{2}{5}) = 1

cos^{2} (\frac{2}{5})

を右側に移動します

u^{2} + cos^{2} (\frac{2}{5}) = 1

両辺から

cos^{2} (\frac{2}{5})

を引く

u^{2} + cos^{2} (\frac{2}{5}) - cos^{2} (\frac{2}{5}) = 1 - cos^{2} (\frac{2}{5})

簡素化

u^{2} = 1 - cos^{2} (\frac{2}{5})

u^{2} = 1 - cos^{2} (\frac{2}{5})

x^{2} = f (a)

の場合, 解は

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

u = 1 - cos^{2} (\frac{2}{5}), u = - 1 - cos^{2} (\frac{2}{5})

代用を戻す

u = sin (x)

sin (x) = 1 - cos^{2} (\frac{2}{5}), sin (x) = - 1 - cos^{2} (\frac{2}{5})

sin (x) = 1 - cos^{2} (\frac{2}{5}), sin (x) = - 1 - cos^{2} (\frac{2}{5})

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

sin (x) = 1 - cos^{2} (\frac{2}{5})

三角関数の逆数プロパティを適用する

sin (x) = 1 - cos^{2} (\frac{2}{5})

以下の一般解

sin (x) = 1 - cos^{2} (\frac{2}{5})

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

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

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

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

sin (x) = - 1 - cos^{2} (\frac{2}{5})

三角関数の逆数プロパティを適用する

sin (x) = - 1 - cos^{2} (\frac{2}{5})

以下の一般解

sin (x) = - 1 - cos^{2} (\frac{2}{5})

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

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

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

すべての解を組み合わせる

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

10進法形式で解を証明する

x = 0.4 + 2 πn, x = π - 0.4 + 2 πn, x = - 0.4 + 2 πn, x = π + 0.4 + 2 πn

グラフ

人気の例

-4sin(x)+3cos(x)=0

sin(x)-1=0,sin(x)-1=0

2sqrt(3)cos(2x)=-3