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受欢迎的三角函数 >

(0.866)/(sin(x))=1.53

解答

\frac{0.866}{sin ( x )} = 1.53

解答

x = 0.60166 \dots + 2 πn, x = π - 0.60166 \dots + 2 πn

+1

度数

x = 34.47267 \dots^{\circ} + 36 0^{\circ} n, x = 145.52732 \dots^{\circ} + 36 0^{\circ} n

求解步骤

\frac{0.866}{sin ( x )} = 1.53

在两边乘以

sin (x)

\frac{0.866}{sin ( x )} = 1.53

在两边乘以

sin (x)

\frac{0.866}{sin ( x )} sin (x) = 1.53 sin (x)

化简

0.866 = 1.53 sin (x)

0.866 = 1.53 sin (x)

交换两边

1.53 sin (x) = 0.866

在两边乘以

1000

1.53 sin (x) = 0.866

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

1.53 sin (x) \cdot 1000 = 0.866 \cdot 1000

整理后得

1530 sin (x) = 866

1530 sin (x) = 866

两边除以

1530

1530 sin (x) = 866

两边除以

1530

\frac{1530 sin ( x )}{1530} = \frac{866}{1530}

化简

sin (x) = \frac{433}{765}

sin (x) = \frac{433}{765}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{0.866}{sin ( x )}

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

sin (x) = \frac{433}{765}

使用反三角函数性质

sin (x) = \frac{433}{765}

sin (x) = \frac{433}{765}

的通解

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

x = arcsin (\frac{433}{765}) + 2 πn, x = π - arcsin (\frac{433}{765}) + 2 πn

x = arcsin (\frac{433}{765}) + 2 πn, x = π - arcsin (\frac{433}{765}) + 2 πn

以小数形式表示解

x = 0.60166 \dots + 2 πn, x = π - 0.60166 \dots + 2 πn

作图

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