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人気のある三角関数 >

cos(3x)= 1/5

解

cos (3 x) = \frac{1}{5}

解

x = \frac{1.36943 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.36943 \dots}{3} + \frac{2 πn}{3}

+1

度

x = 26.15434 \dots^{\circ} + 12 0^{\circ} n, x = 93.84565 \dots^{\circ} + 12 0^{\circ} n

解答ステップ

cos (3 x) = \frac{1}{5}

三角関数の逆数プロパティを適用する

cos (3 x) = \frac{1}{5}

以下の一般解

cos (3 x) = \frac{1}{5}

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

3 x = arccos (\frac{1}{5}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{5}) + 2 πn

3 x = arccos (\frac{1}{5}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{5}) + 2 πn

解く

3 x = arccos (\frac{1}{5}) + 2 πn : x = \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

3

3 x = arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

解く

3 x = 2 π - arccos (\frac{1}{5}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

3

3 x = 2 π - arccos (\frac{1}{5}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{5} )}{3} + \frac{2 πn}{3}

10進法形式で解を証明する

x = \frac{1.36943 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.36943 \dots}{3} + \frac{2 πn}{3}

グラフ

人気の例

cos^2(x)-5cos(x)+6=0

cos^{2} (x) - 5 cos (x) + 6 = 0

cot^2(x/2)=3,0,0<= x<= 360

cot^{2} (\frac{x}{2}) = 3, 0, 0 \leq x \leq 360

sin(x)=(123sin(70))/(184.5)

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

cot^2(θ)=cot(θ),0<= θ<= 2pi

cot^{2} (θ) = cot (θ), 0 \leq θ \leq 2 π

cos (x) = \frac{9}{19}