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شائع علم المثلثات >

2/(3(0.22856^2)sin(60))

الحلّ

\frac{2}{3 \cdot ( 0.2285 6 ^{2} ) \cdot sin ( 6 0 ^{\circ} )}

الحلّ

\frac{625000000 3}{73462041}

+1

عشري

14.73593 \dots

خطوات الحلّ

\frac{2}{3 ( 0.2285 6 ^{2} ) sin ( 6 0 ^{\circ} )}

= \frac{2}{3 ( \frac{2857}{12500} ) ^{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{2}{3 ( \frac{2857}{12500} ) ^{2} \frac{3}{2}}

\frac{2}{3 ( \frac{2857}{12500} ) ^{2} \frac{3}{2}}

بسّط:

\frac{625000000 3}{73462041}

\frac{2}{3 ( \frac{2857}{12500} ) ^{2} \frac{3}{2}}

3 (\frac{2857}{12500})^{2} \frac{3}{2}

اضرب بـ:

\frac{24487347 3}{312500000}

3 (\frac{2857}{12500})^{2} \frac{3}{2}

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

:اضرب كسور

= \frac{3 \cdot 3 ( \frac{2857}{12500} ) ^{2}}{2}

(\frac{2857}{12500})^{2} = \frac{285 7 ^{2}}{1250 0 ^{2}}

(\frac{2857}{12500})^{2}

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

:فعّل قانون القوى

= \frac{285 7 ^{2}}{1250 0 ^{2}}

= \frac{3 3 \frac{285 7 ^{2}}{1250 0 ^{2}}}{2}

3 \cdot 3 \cdot \frac{285 7 ^{2}}{1250 0 ^{2}}

اضرب بـ:

\frac{24487347 3}{156250000}

3 \cdot 3 \cdot \frac{285 7 ^{2}}{1250 0 ^{2}}

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

:اضرب كسور

= \frac{285 7 ^{2} 3 \cdot 3}{1250 0 ^{2}}

285 7^{2} 3 \cdot 3 = 244873473

285 7^{2} 3 \cdot 3

285 7^{2} = 8162449

= 8162449 \cdot 33

8162449 \cdot 3 = 24487347 :

اضرب الأعداد

= 244873473

= \frac{24487347 3}{1250 0 ^{2}}

1250 0^{2} = 156250000

= \frac{24487347 3}{156250000}

= \frac{\frac{24487347 3}{156250000}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{24487347 3}{156250000 \cdot 2}

156250000 \cdot 2 = 312500000 :

اضرب الأعداد

= \frac{24487347 3}{312500000}

= \frac{2}{\frac{24487347 3}{312500000}}

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

: استخدم ميزات الكسور التالية

= \frac{2 \cdot 312500000}{24487347 3}

2 \cdot 312500000 = 625000000 :

اضرب الأعداد

= \frac{625000000}{24487347 3}

\frac{625000000}{24487347 3}

حوّل لصيغة عدد كسريّ:

\frac{625000000 3}{73462041}

\frac{625000000}{24487347 3}

\frac{3}{3}

اضرب بالمرافق

= \frac{625000000 3}{24487347 3 3}

2448734733 = 73462041

2448734733

a a = a

:فعْل قانون الجذور

33 = 3

= 24487347 \cdot 3

24487347 \cdot 3 = 73462041 :

اضرب الأعداد

= 73462041

= \frac{625000000 3}{73462041}

= \frac{625000000 3}{73462041}

= \frac{625000000 3}{73462041}

أمثلة شائعة

5sin^2((3pi)/2)+3cos^2(4pi)-7tan(pi/4)

5 sin^{2} (\frac{3 π}{2}) + 3 cos^{2} (4 π) - 7 tan (\frac{π}{4})

sin^{2} (6 5^{\circ})

cos (6 0^{\circ}) sin (3 0^{\circ})

2 - 2 cosh (0 - 2)

- 100 sin (6 0^{\circ})