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شائع علم المثلثات >

(sin(x))/(120)=(sin(60))/(300)

الحلّ

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

الحلّ

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

+1

راديان

x = 0.35374 \dots + 2 πn, x = π - 0.35374 \dots + 2 πn

خطوات الحلّ

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\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{3}{2}

= \frac{3}{2}

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

100

اضرب الطرفين بـ

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

100

اضرب الطرفين بـ

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

بسّط

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

\frac{sin ( x )}{120} \cdot 100

بسّط:

\frac{5 sin ( x )}{6}

\frac{sin ( x )}{120} \cdot 100

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

:اضرب كسور

= \frac{sin ( x ) \cdot 100}{120}

20 :

إلغ العوامل المشتركة

= \frac{5 sin ( x )}{6}

\frac{\frac{3}{2}}{300} \cdot 100

بسّط:

\frac{3}{6}

\frac{\frac{3}{2}}{300} \cdot 100

\frac{\frac{3}{2}}{300} = \frac{3}{600}

\frac{\frac{3}{2}}{300}

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

: استخدم ميزات الكسور التالية

= \frac{3}{2 \cdot 300}

2 \cdot 300 = 600 :

اضرب الأعداد

= \frac{3}{600}

= 100 \cdot \frac{3}{600}

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

:اضرب كسور

= \frac{3 \cdot 100}{600}

100 :

إلغ العوامل المشتركة

= \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

6

اضرب الطرفين بـ

\frac{5 sin ( x )}{6} = \frac{3}{6}

6

اضرب الطرفين بـ

\frac{6 \cdot 5 sin ( x )}{6} = \frac{6 3}{6}

بسّط

5 sin (x) = 3

5 sin (x) = 3

5

اقسم الطرفين على

5 sin (x) = 3

5

اقسم الطرفين على

\frac{5 sin ( x )}{5} = \frac{3}{5}

بسّط

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Apply trig inverse properties

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5} :

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{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

رسم

أمثلة شائعة

8sin(θ)+15cos(θ)=0

8 sin (θ) + 15 cos (θ) = 0

sin (t) = \frac{3}{7}

cos(2x-1)=sin(3x+6)

cos (2 x - 1) = sin (3 x + 6)

(sin(b))/(300)=(sin(49))/(500)

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

sin(θ)=cos(2θ+60)

sin (θ) = cos (2 θ + 6 0^{\circ})