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شائع علم المثلثات >

2/3 =(sin(x))/(sin(135))

الحلّ

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

الحلّ

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

+1

راديان

x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

خطوات الحلّ

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

بدّل الأطراف

\frac{sin ( x )}{sin ( 13 5 ^{\circ} )} = \frac{2}{3}

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

\frac{sin ( x )}{\frac{2}{2}} = \frac{2}{3}

\frac{2}{2}

اضرب الطرفين بـ

\frac{sin ( x )}{\frac{2}{2}} = \frac{2}{3}

\frac{2}{2}

اضرب الطرفين بـ

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}} = \frac{2 \cdot \frac{2}{2}}{3}

بسّط

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}} = \frac{2 \cdot \frac{2}{2}}{3}

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}}

بسّط:

sin (x)

\frac{sin ( x ) \frac{2}{2}}{\frac{2}{2}}

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

: استخدم ميزات الكسور التالية

= \frac{sin ( x ) \frac{2}{2} \cdot 2}{2}

sin (x) \frac{2}{2} \cdot 2

اضرب بـ:

2 sin (x)

sin (x) \frac{2}{2} \cdot 2

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

:اضرب كسور

= \frac{2 sin ( x ) \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 2 sin (x)

= \frac{2 sin ( x )}{2}

2 :

إلغ العوامل المشتركة

= sin (x)

\frac{2 \cdot \frac{2}{2}}{3}

بسّط:

\frac{2}{3}

\frac{2 \cdot \frac{2}{2}}{3}

2 \cdot \frac{2}{2}

اضرب بـ:

2

2 \cdot \frac{2}{2}

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

:اضرب كسور

= \frac{2 \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 2

= \frac{2}{3}

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

Apply trig inverse properties

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3} :

حلول عامّة لـ

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

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

رسم

أمثلة شائعة

sin(x)+2(cos(x))^2=1

sin (x) + 2 (cos (x))^{2} = 1

a sin (2 θ) = 0

cos(2x)=0,x<= 2pi,0

cos (2 x) = 0, x \leq 2 π, 0

7+csc(2x)=3cot^2(2x)

7 + csc (2 x) = 3 cot^{2} (2 x)

cos(θ)=cos(pi/(13))

cos (θ) = cos (\frac{π}{13})