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(sin(57.22))/(31.5)=(sin(Q))/(24.4)

解答

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( Q )}{24.4}

解答

Q = 0.70923 \dots + 36 0^{\circ} n, Q = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

+1

弧度

Q = 0.70923 \dots + 2 πn, Q = π - 0.70923 \dots + 2 πn

求解步骤

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( Q )}{24.4}

交换两边

\frac{sin ( Q )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

在两边乘以

24.4

\frac{sin ( Q )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

在两边乘以

24.4

\frac{24.4 sin ( Q )}{24.4} = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

化简

sin (Q) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

sin (Q) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

使用反三角函数性质

sin (Q) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

sin (Q) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

的通解

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

Q = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, Q = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

Q = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, Q = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

以小数形式表示解

Q = 0.70923 \dots + 36 0^{\circ} n, Q = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

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