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受欢迎的三角函数 >

(sin(118))/(18.03)=(sin(b))/(17)

解答

\frac{sin ( 11 8 ^{\circ} )}{18.03} = \frac{sin ( b ^{\circ} )}{17}

解答

b \in R 无解

求解步骤

\frac{sin ( 11 8 ^{\circ} )}{18.03} = \frac{sin ( b ^{\circ} )}{17}

交换两边

\frac{sin ( b ^{\circ} )}{17} = \frac{sin ( 11 8 ^{\circ} )}{18.03}

在两边乘以

17

\frac{sin ( b ^{\circ} )}{17} = \frac{sin ( 11 8 ^{\circ} )}{18.03}

在两边乘以

17

\frac{17 sin ( b ^{\circ} )}{17} = \frac{17 sin ( 11 8 ^{\circ} )}{18.03}

化简

sin (b^{\circ}) = \frac{17 sin ( 11 8 ^{\circ} )}{18.03}

sin (b^{\circ}) = \frac{17 sin ( 11 8 ^{\circ} )}{18.03}

使用反三角函数性质

sin (b^{\circ}) = \frac{17 sin ( 11 8 ^{\circ} )}{18.03}

sin (b^{\circ}) = \frac{17 sin ( 11 8 ^{\circ} )}{18.03}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

b^{\circ} = arcsin (\frac{17 sin ( 11 8 ^{\circ} )}{18.03}) + 36 0^{\circ} n, b^{\circ} = 18 0^{\circ} - arcsin (\frac{17 sin ( 11 8 ^{\circ} )}{18.03}) + 36 0^{\circ} n

b^{\circ} = arcsin (\frac{17 sin ( 11 8 ^{\circ} )}{18.03}) + 36 0^{\circ} n, b^{\circ} = 18 0^{\circ} - arcsin (\frac{17 sin ( 11 8 ^{\circ} )}{18.03}) + 36 0^{\circ} n

b \in R 无解

作图

流行的例子

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4 5^{\circ} = 57. 7^{\circ} + arctan (\frac{3.5}{x}) - arctan (\frac{175}{x})

\frac{1}{2} - cos (\frac{x}{2}) = 0

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