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人気のある三角関数 >

7cos(3x)=2,0<= x<2pi

解

7 cos (3 x) = 2, 0 \leq x < 2 π

解

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

+1

度

x = 24.46615 \dots^{\circ}, x = 95.53384 \dots^{\circ}, x = 144.46615 \dots^{\circ}, x = 215.53384 \dots^{\circ}, x = 264.46615 \dots^{\circ}, x = 335.53384 \dots^{\circ}

解答ステップ

7 cos (3 x) = 2, 0 \leq x < 2 π

以下で両辺を割る

7

7 cos (3 x) = 2

以下で両辺を割る

7

\frac{7 cos ( 3 x )}{7} = \frac{2}{7}

簡素化

cos (3 x) = \frac{2}{7}

cos (3 x) = \frac{2}{7}

三角関数の逆数プロパティを適用する

cos (3 x) = \frac{2}{7}

以下の一般解

cos (3 x) = \frac{2}{7}

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

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

解く

3 x = arccos (\frac{2}{7}) + 2 πn : x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{2}{7}) + 2 πn

以下で両辺を割る

3

3 x = arccos (\frac{2}{7}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

解く

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

以下で両辺を割る

3

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

簡素化

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

範囲の解答

0 \leq x < 2 π

x = \frac{arccos ( \frac{2}{7} )}{3}, x = \frac{2 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 2 π}{3}, x = \frac{4 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 4 π}{3}, x = \frac{6 π - arccos ( \frac{2}{7} )}{3}

10進法形式で解を証明する

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

グラフ

人気の例

6 cos (2 x) = 3

arctan(x/(42))=57

arctan (\frac{x}{42}) = 57

3 tan^{2} (x) = 19

3.6=0.116cos(4.17x)

3.6 = 0.116 cos (4.17 x)

cos(x)=(sqrt(3))/2 ,sin(2x),-90<= x<= 0

cos (x) = \frac{3}{2}, sin (2 x), - 9 0^{\circ} \leq x \leq 0^{\circ}