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人気のある三角関数 >

5sin(4x)=2

解

5 sin (4 x) = 2

解

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

+1

度

x = 5.89454 \dots^{\circ} + 9 0^{\circ} n, x = 39.10545 \dots^{\circ} + 9 0^{\circ} n

解答ステップ

5 sin (4 x) = 2

以下で両辺を割る

5

5 sin (4 x) = 2

以下で両辺を割る

5

\frac{5 sin ( 4 x )}{5} = \frac{2}{5}

簡素化

sin (4 x) = \frac{2}{5}

sin (4 x) = \frac{2}{5}

三角関数の逆数プロパティを適用する

sin (4 x) = \frac{2}{5}

以下の一般解

sin (4 x) = \frac{2}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

4 x = arcsin (\frac{2}{5}) + 2 πn, 4 x = π - arcsin (\frac{2}{5}) + 2 πn

4 x = arcsin (\frac{2}{5}) + 2 πn, 4 x = π - arcsin (\frac{2}{5}) + 2 πn

解く

4 x = arcsin (\frac{2}{5}) + 2 πn : x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

4 x = arcsin (\frac{2}{5}) + 2 πn

以下で両辺を割る

4

4 x = arcsin (\frac{2}{5}) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{2 πn}{4}

簡素化

x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

解く

4 x = π - arcsin (\frac{2}{5}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

4 x = π - arcsin (\frac{2}{5}) + 2 πn

以下で両辺を割る

4

4 x = π - arcsin (\frac{2}{5}) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{2 πn}{4}

簡素化

x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

10進法形式で解を証明する

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

グラフ

人気の例

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