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人気のある三角関数 >

cos(2x)= 3/5

解

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

解

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

+1

度

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n, x = 153.43494 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

解く

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

2 x = arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

2 x = arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

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

簡素化

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

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

解く

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

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

以下で両辺を割る

2

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

以下で両辺を割る

2

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

簡素化

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

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

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

10進法形式で解を証明する

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

グラフ

人気の例

- 4 cos (2 x) = 0

solvefor x,arcsin(y)=arcsin(x)+pi/3

so l v e f or x, arcsin (y) = arcsin (x) + \frac{π}{3}

solvefor t,f=cos(bt)

so l v e f or t, f = cos (b t)

sqrt(3)cos(x)+sin(x)=0

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

sqrt(3)sec(2x)=2

3 sec (2 x) = 2