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人気のある三角関数 >

cos(2θ)= 20/29

解

cos (2 θ) = \frac{20}{29}

解

θ = \frac{0.80978 \dots}{2} + πn, θ = π - \frac{0.80978 \dots}{2} + πn

+1

度

θ = 23.19859 \dots^{\circ} + 18 0^{\circ} n, θ = 156.80140 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

cos (2 θ) = \frac{20}{29}

三角関数の逆数プロパティを適用する

cos (2 θ) = \frac{20}{29}

以下の一般解

cos (2 θ) = \frac{20}{29}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 θ = arccos (\frac{20}{29}) + 2 πn, 2 θ = 2 π - arccos (\frac{20}{29}) + 2 πn

2 θ = arccos (\frac{20}{29}) + 2 πn, 2 θ = 2 π - arccos (\frac{20}{29}) + 2 πn

解く

2 θ = arccos (\frac{20}{29}) + 2 πn : θ = \frac{arccos ( \frac{20}{29} )}{2} + πn

2 θ = arccos (\frac{20}{29}) + 2 πn

以下で両辺を割る

2

2 θ = arccos (\frac{20}{29}) + 2 πn

以下で両辺を割る

2

\frac{2 θ}{2} = \frac{arccos ( \frac{20}{29} )}{2} + \frac{2 πn}{2}

簡素化

θ = \frac{arccos ( \frac{20}{29} )}{2} + πn

θ = \frac{arccos ( \frac{20}{29} )}{2} + πn

解く

2 θ = 2 π - arccos (\frac{20}{29}) + 2 πn : θ = π - \frac{arccos ( \frac{20}{29} )}{2} + πn

2 θ = 2 π - arccos (\frac{20}{29}) + 2 πn

以下で両辺を割る

2

2 θ = 2 π - arccos (\frac{20}{29}) + 2 πn

以下で両辺を割る

2

\frac{2 θ}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{20}{29} )}{2} + \frac{2 πn}{2}

簡素化

θ = π - \frac{arccos ( \frac{20}{29} )}{2} + πn

θ = π - \frac{arccos ( \frac{20}{29} )}{2} + πn

θ = \frac{arccos ( \frac{20}{29} )}{2} + πn, θ = π - \frac{arccos ( \frac{20}{29} )}{2} + πn

10進法形式で解を証明する

θ = \frac{0.80978 \dots}{2} + πn, θ = π - \frac{0.80978 \dots}{2} + πn

グラフ

人気の例

sin(x)=(sqrt(2))/4

sin (x) = \frac{2}{4}

2 tan (2 x) - 6 = 0

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8 sin (θ) + 15 cos (θ) = 18

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