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受欢迎的三角函数 >

(sin(80))/5 =(sin(x))/4

解答

\frac{sin ( 8 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}

解答

x = 0.90730 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.90730 \dots + 36 0^{\circ} n

+1

弧度

x = 0.90730 \dots + 2 πn, x = π - 0.90730 \dots + 2 πn

求解步骤

\frac{sin ( 8 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}

交换两边

\frac{sin ( x )}{4} = \frac{sin ( 8 0 ^{\circ} )}{5}

在两边乘以

4

\frac{sin ( x )}{4} = \frac{sin ( 8 0 ^{\circ} )}{5}

在两边乘以

4

\frac{4 sin ( x )}{4} = \frac{4 sin ( 8 0 ^{\circ} )}{5}

化简

sin (x) = \frac{4 sin ( 8 0 ^{\circ} )}{5}

sin (x) = \frac{4 sin ( 8 0 ^{\circ} )}{5}

使用反三角函数性质

sin (x) = \frac{4 sin ( 8 0 ^{\circ} )}{5}

sin (x) = \frac{4 sin ( 8 0 ^{\circ} )}{5}

的通解

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

x = arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n

以小数形式表示解

x = 0.90730 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.90730 \dots + 36 0^{\circ} n

作图

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