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شائع علم المثلثات >

((30)^2sin^2(30))/(2*9.81^2)

الحلّ

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

الحلّ

\frac{125000}{106929}

+1

عشري

1.16899 \dots

خطوات الحلّ

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

= \frac{3 0 ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 ( \frac{981}{100} ) ^{2}}

استخدم المتطابقة الأساسيّة التالية:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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{1}{2}

= \frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

بسّط:

\frac{125000}{106929}

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

3 0^{2}

حلل إلى عوامل:

2^{2} \cdot 3^{2} \cdot 5^{2}

30 = 2 \cdot 3 \cdot 5

حلّل إلى عوامل

= (2 \cdot 3 \cdot 5)^{2}

(ab)^{c} = a^{c} b^{c}

:فعّل قانون القوى

= 2^{2} \cdot 3^{2} \cdot 5^{2}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

2 :

إلغ العوامل المشتركة

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{( \frac{981}{100} ) ^{2}}

(\frac{981}{100})^{2} = \frac{98 1 ^{2}}{10 0 ^{2}}

(\frac{981}{100})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:فعّل قانون القوى

= \frac{98 1 ^{2}}{10 0 ^{2}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{\frac{98 1 ^{2}}{10 0 ^{2}}}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:فعّل قانون القوى

= \frac{1 ^{2}}{2 ^{2}}

1^{a} = 1

فعّل القانون

1^{2} = 1

= \frac{1}{2 ^{2}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{\frac{98 1 ^{2}}{10 0 ^{2}}}

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

: استخدم ميزات الكسور التالية

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0 ^{2}}{98 1 ^{2}}

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2}

بسّط:

5^{6} \cdot 3^{2} \cdot 4^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2}

100 = 5^{2} \cdot 4 :

حلّل العدد لعوامله الأوّليّة

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2} \cdot 4)^{2}

(ab)^{c} = a^{c} b^{c}

:فعّل قانون القوى

(5^{2} \cdot 4)^{2} = (5^{2})^{2} \cdot 4^{2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2})^{2} \cdot 4^{2}

(a^{b})^{c} = a^{b c}

:فعّل قانون القوى

(5^{2})^{2} = 5^{2 \cdot 2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 \cdot 2} \cdot 4^{2}

بسّط

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{4} \cdot 4^{2}

a^{b} \cdot a^{c} = a^{b + c}

:فعّل قانون القوى

5^{2} \cdot 5^{4} = 5^{2 + 4}

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 + 4} \cdot 4^{2}

2 + 4 = 6 :

اجمع الأعداد

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{98 1 ^{2}}

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

اضرب بـ:

1125000

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

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

:اضرب كسور

= \frac{1 \cdot 3 ^{2} \cdot 2 \cdot 5 ^{6} \cdot 4 ^{2}}{2 ^{2}}

1 \cdot 2 = 2 :

اضرب الأعداد

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2}{2 ^{2}}

2 :

إلغ العوامل المشتركة

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2}}{2}

4^{2}

حلل إلى عوامل:

2^{4}

4 = 2^{2}

حلّل إلى عوامل

= (2^{2})^{2}

(2^{2})^{2}

بسّط:

2^{4}

(2^{2})^{2}

(a^{b})^{c} = a^{b c}

:فعّل قانون القوى

= 2^{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= 2^{4}

= 2^{4}

= \frac{5 ^{6} \cdot 2 ^{4} \cdot 3 ^{2}}{2}

2 :

إلغ العوامل المشتركة

= 5^{6} \cdot 2^{3} \cdot 3^{2}

5^{6} = 15625

= 2^{3} \cdot 3^{2} \cdot 15625

2^{3} = 8

= 3^{2} \cdot 15625 \cdot 8

3^{2} = 9

= 15625 \cdot 8 \cdot 9

15625 \cdot 8 \cdot 9 = 1125000 :

اضرب الأعداد

= 1125000

= \frac{1125000}{98 1 ^{2}}

1125000

حلل إلى عوامل:

5^{6} \cdot 2^{3} \cdot 3^{2}

1125000 = 5^{6} \cdot 2^{3} \cdot 3^{2}

حلّل إلى عوامل

98 1^{2}

حلل إلى عوامل:

3^{4} \cdot 10 9^{2}

981 = 3^{2} \cdot 109

حلّل إلى عوامل

= (3^{2} \cdot 109)^{2}

(ab)^{c} = a^{c} b^{c}

:فعّل قانون القوى

= 10 9^{2} (3^{2})^{2}

(3^{2})^{2}

بسّط:

3^{4}

(3^{2})^{2}

(a^{b})^{c} = a^{b c}

:فعّل قانون القوى

= 3^{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= 3^{4}

= 3^{4} \cdot 10 9^{2}

= \frac{5 ^{6} \cdot 2 ^{3} \cdot 3 ^{2}}{3 ^{4} \cdot 10 9 ^{2}}

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}}

اختزل:

\frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{3 ^{2}}{3 ^{4}} = \frac{1}{3 ^{4 - 2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{10 9 ^{2} \cdot 3 ^{4 - 2}}

4 - 2 = 2 :

اطرح الأعداد

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

5^{6} \cdot 2^{3} = 125000

5^{6} \cdot 2^{3}

5^{6} = 15625

= 2^{3} \cdot 15625

2^{3} = 8

= 15625 \cdot 8

15625 \cdot 8 = 125000 :

اضرب الأعداد

= 125000

= \frac{125000}{3 ^{2} \cdot 10 9 ^{2}}

3^{2} \cdot 10 9^{2} = 106929

3^{2} \cdot 10 9^{2}

3^{2} = 9

= 10 9^{2} \cdot 9

10 9^{2} = 11881

= 9 \cdot 11881

9 \cdot 11881 = 106929 :

اضرب الأعداد

= 106929

= \frac{125000}{106929}

= \frac{125000}{106929}

أمثلة شائعة

tan (4 1^{\circ}) \cdot 3

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11 \cdot sin (6 5^{\circ})

tan(60)+csc(60)

tan (6 0^{\circ}) + csc (6 0^{\circ})