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受欢迎的三角函数 >

9.2sin(t)+23.2=14.365

解答

9.2 sin (t) + 23.2 = 14.365

解答

t = - 1.28816 \dots + 2 πn, t = π + 1.28816 \dots + 2 πn

+1

度数

t = - 73.80665 \dots^{\circ} + 36 0^{\circ} n, t = 253.80665 \dots^{\circ} + 36 0^{\circ} n

求解步骤

9.2 sin (t) + 23.2 = 14.365

在两边乘以

1000

9.2 sin (t) + 23.2 = 14.365

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

9.2 sin (t) \cdot 1000 + 23.2 \cdot 1000 = 14.365 \cdot 1000

整理后得

9200 sin (t) + 23200 = 14365

9200 sin (t) + 23200 = 14365

将

23200

到右边

9200 sin (t) + 23200 = 14365

两边减去

23200

9200 sin (t) + 23200 - 23200 = 14365 - 23200

化简

9200 sin (t) = - 8835

9200 sin (t) = - 8835

两边除以

9200

9200 sin (t) = - 8835

两边除以

9200

\frac{9200 sin ( t )}{9200} = \frac{- 8835}{9200}

化简

\frac{9200 sin ( t )}{9200} = \frac{- 8835}{9200}

化简

\frac{9200 sin ( t )}{9200} : sin (t)

\frac{9200 sin ( t )}{9200}

数字相除:

\frac{9200}{9200} = 1

= sin (t)

化简

\frac{- 8835}{9200} : - \frac{1767}{1840}

\frac{- 8835}{9200}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{8835}{9200}

约分:

5

= - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

使用反三角函数性质

sin (t) = - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

的通解

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

t = arcsin (- \frac{1767}{1840}) + 2 πn, t = π + arcsin (\frac{1767}{1840}) + 2 πn

t = arcsin (- \frac{1767}{1840}) + 2 πn, t = π + arcsin (\frac{1767}{1840}) + 2 πn

以小数形式表示解

t = - 1.28816 \dots + 2 πn, t = π + 1.28816 \dots + 2 πn

作图

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