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5.8=11.8sin(3.78*t)

解答

5.8 = 11.8 sin (3.78 \cdot t)

解答

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

度数

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

求解步骤

5.8 = 11.8 sin (3.78 t)

交换两边

11.8 sin (3.78 t) = 5.8

在两边乘以

10

11.8 sin (3.78 t) = 5.8

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

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

整理后得

118 sin (3.78 t) = 58

118 sin (3.78 t) = 58

两边除以

118

118 sin (3.78 t) = 58

两边除以

118

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

化简

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

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

使用反三角函数性质

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

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

的通解

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

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

两边除以

3.78

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

两边除以

3.78

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

化简

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

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

两边除以

3.78

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

两边除以

3.78

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

化简

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}

以小数形式表示解

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}

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