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25picos((pi 1/2)/2)

الحلّ

25 π cos (\frac{π \frac{1}{2}}{2})

الحلّ

\frac{25 2 π}{2}

+1

العشري

55.53603 \dots

خطوات الحلّ

25 π cos (\frac{π \frac{1}{2}}{2})

بسّط:

\frac{π \frac{1}{2}}{2} = \frac{π}{4}

\frac{π \frac{1}{2}}{2}

π \frac{1}{2}

اضرب بـ:

\frac{π}{2}

π \frac{1}{2}

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

:اضرب كسور

= \frac{1 π}{2}

1 π = π :

اضرب

= \frac{π}{2}

= \frac{\frac{π}{2}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{π}{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{π}{4}

= 25 π cos (\frac{π}{4})

استخدم المتطابقة الأساسيّة التالية:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= 25 π \frac{2}{2}

25 π \frac{2}{2}

بسّط:

\frac{25 2 π}{2}

25 π \frac{2}{2}

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

:اضرب كسور

= \frac{2 \cdot 25 π}{2}

:فعْل قانون الجذور

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

= \frac{25 \cdot 2 ^{\frac{1}{2}} π}{2}

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

:فعّل قانون القوى

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

= \frac{25 π}{2 ^{1 - \frac{1}{2}}}

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{25 π}{2 ^{\frac{1}{2}}}

:فعْل قانون الجذور

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

= \frac{25 π}{2}

\frac{25 π}{2}

حوّل لصيغة عدد كسريّ:

\frac{25 2 π}{2}

\frac{25 π}{2}

\frac{2}{2}

اضرب بالمرافق

= \frac{25 π 2}{2 2}

22 = 2

22

a a = a

:فعْل قانون الجذور

22 = 2

= 2

= \frac{25 2 π}{2}

= \frac{25 2 π}{2}

= \frac{25 2 π}{2}

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