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شائع علم المثلثات >

(sin(θ))/(140)=(sin(110))/(622)

الحلّ

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

الحلّ

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

+1

راديان

θ = 0.21311 \dots + 2 πn, θ = π - 0.21311 \dots + 2 πn

خطوات الحلّ

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

10

اضرب الطرفين بـ

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

10

اضرب الطرفين بـ

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

بسّط

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

\frac{sin ( θ )}{140} \cdot 10

بسّط:

\frac{sin ( θ )}{14}

\frac{sin ( θ )}{140} \cdot 10

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{sin ( θ ) \cdot 10}{140}

10 :

إلغ العوامل المشتركة

= \frac{sin ( θ )}{14}

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

بسّط:

\frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:اضرب كسور

= \frac{sin ( 11 0 ^{\circ} ) \cdot 10}{622}

2 :

إلغ العوامل المشتركة

= \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

14

اضرب الطرفين بـ

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

14

اضرب الطرفين بـ

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

بسّط

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

\frac{14 sin ( θ )}{14}

بسّط:

sin (θ)

\frac{14 sin ( θ )}{14}

\frac{14}{14} = 1 :

اقسم الأعداد

= sin (θ)

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

بسّط:

\frac{70 sin ( 11 0 ^{\circ} )}{311}

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

14 \cdot 5 = 70 :

اضرب الأعداد

= \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

Apply trig inverse properties

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311} :

حلول عامّة لـ

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

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

رسم

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