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人気のある三角関数 >

csc^2(t)=3

解

csc^{2} (t) = 3

解

t = 0.61547 \dots + 2 πn, t = π - 0.61547 \dots + 2 πn, t = - 0.61547 \dots + 2 πn, t = π + 0.61547 \dots + 2 πn

+1

度

t = 35.26438 \dots^{\circ} + 36 0^{\circ} n, t = 144.73561 \dots^{\circ} + 36 0^{\circ} n, t = - 35.26438 \dots^{\circ} + 36 0^{\circ} n, t = 215.26438 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

csc^{2} (t) = 3

置換で解く

csc^{2} (t) = 3

仮定:

csc (t) = u

u^{2} = 3

u^{2} = 3 : u = 3, u = - 3

u^{2} = 3

x^{2} = f (a)

の場合, 解は

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

u = 3, u = - 3

代用を戻す

u = csc (t)

csc (t) = 3, csc (t) = - 3

csc (t) = 3, csc (t) = - 3

csc (t) = 3 : t = arccsc (3) + 2 πn, t = π - arccsc (3) + 2 πn

csc (t) = 3

三角関数の逆数プロパティを適用する

csc (t) = 3

以下の一般解

csc (t) = 3

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

t = arccsc (3) + 2 πn, t = π - arccsc (3) + 2 πn

t = arccsc (3) + 2 πn, t = π - arccsc (3) + 2 πn

csc (t) = - 3 : t = arccsc (- 3) + 2 πn, t = π + arccsc (3) + 2 πn

csc (t) = - 3

三角関数の逆数プロパティを適用する

csc (t) = - 3

以下の一般解

csc (t) = - 3

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

t = arccsc (- 3) + 2 πn, t = π + arccsc (3) + 2 πn

t = arccsc (- 3) + 2 πn, t = π + arccsc (3) + 2 πn

すべての解を組み合わせる

t = arccsc (3) + 2 πn, t = π - arccsc (3) + 2 πn, t = arccsc (- 3) + 2 πn, t = π + arccsc (3) + 2 πn

10進法形式で解を証明する

t = 0.61547 \dots + 2 πn, t = π - 0.61547 \dots + 2 πn, t = - 0.61547 \dots + 2 πn, t = π + 0.61547 \dots + 2 πn

グラフ

人気の例

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3 cos (x) = cos (x) - 1

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cos (x) = 0.9224

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