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شائع علم المثلثات >

(sin(180)}{20}=\frac{sin(a))/8

الحلّ

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

الحلّ

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

+1

راديان

a = 0 + 2 πn, a = π + 2 πn

خطوات الحلّ

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

sin (18 0^{\circ}) = 0

sin (18 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (18 0^{\circ}) = 0

sin (18 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}

= 0

= 0

\frac{0}{20} = \frac{sin ( a )}{8}

بدّل الأطراف

\frac{sin ( a )}{8} = \frac{0}{20}

10

اضرب الطرفين بـ

\frac{sin ( a )}{8} = \frac{0}{20}

10

اضرب الطرفين بـ

\frac{sin ( a )}{8} \cdot 10 = \frac{0}{20} \cdot 10

بسّط

\frac{sin ( a )}{8} \cdot 10 = \frac{0}{20} \cdot 10

\frac{sin ( a )}{8} \cdot 10

بسّط:

\frac{5 sin ( a )}{4}

\frac{sin ( a )}{8} \cdot 10

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

:اضرب كسور

= \frac{sin ( a ) \cdot 10}{8}

2 :

إلغ العوامل المشتركة

= \frac{5 sin ( a )}{4}

\frac{0}{20} \cdot 10

بسّط:

0

\frac{0}{20} \cdot 10

\frac{0}{a} = 0, a \neq = 0

فعّل القانون

\frac{0}{20} = 0

= 0 \cdot 10

0 \cdot a = 0

فعّل القانون

= 0

\frac{5 sin ( a )}{4} = 0

\frac{5 sin ( a )}{4} = 0

\frac{5 sin ( a )}{4} = 0

4

اضرب الطرفين بـ

\frac{5 sin ( a )}{4} = 0

4

اضرب الطرفين بـ

\frac{4 \cdot 5 sin ( a )}{4} = 0 \cdot 4

بسّط

5 sin (a) = 0

5 sin (a) = 0

5

اقسم الطرفين على

5 sin (a) = 0

5

اقسم الطرفين على

\frac{5 sin ( a )}{5} = \frac{0}{5}

بسّط

sin (a) = 0

sin (a) = 0

sin (a) = 0 :

حلول عامّة لـ

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}

a = 0 + 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

a = 0 + 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

a = 0 + 36 0^{\circ} n

حلّ:

a = 36 0^{\circ} n

a = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

a = 36 0^{\circ} n

a = 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

رسم

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