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人気のある三角関数 >

5.8=11.8sin(3.78*t)

解

5.8 = 11.8 sin (3.78 \cdot t)

解

t = \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}

+1

度

t = 7.78859 \dots^{\circ} + 95.23809 \dots^{\circ} n, t = 39.83045 \dots^{\circ} + 95.23809 \dots^{\circ} n

解答ステップ

5.8 = 11.8 sin (3.78 t)

辺を交換する

11.8 sin (3.78 t) = 5.8

以下で両辺を乗じる:

10

11.8 sin (3.78 t) = 5.8

小数点を取り除くには, 小数点以下の各桁に10を乗じます小数点の右側は1桁なので,

10 を乗じます

11.8 sin (3.78 t) \cdot 10 = 5.8 \cdot 10

改良

118 sin (3.78 t) = 58

118 sin (3.78 t) = 58

以下で両辺を割る

118

118 sin (3.78 t) = 58

以下で両辺を割る

118

\frac{118 sin ( 3.78 t )}{118} = \frac{58}{118}

簡素化

sin (3.78 t) = \frac{29}{59}

sin (3.78 t) = \frac{29}{59}

三角関数の逆数プロパティを適用する

sin (3.78 t) = \frac{29}{59}

以下の一般解

sin (3.78 t) = \frac{29}{59}

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

3.78 t = arcsin (\frac{29}{59}) + 2 πn, 3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

3.78 t = arcsin (\frac{29}{59}) + 2 πn, 3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

解く

3.78 t = arcsin (\frac{29}{59}) + 2 πn : t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

3.78 t = arcsin (\frac{29}{59}) + 2 πn

以下で両辺を割る

3.78

3.78 t = arcsin (\frac{29}{59}) + 2 πn

以下で両辺を割る

3.78

\frac{3.78 t}{3.78} = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

簡素化

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

解く

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn : t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

以下で両辺を割る

3.78

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

以下で両辺を割る

3.78

\frac{3.78 t}{3.78} = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

簡素化

t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

10進法形式で解を証明する

t = \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}

グラフ

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