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شائع علم المثلثات >

500sec^2(arctan(1/2))(12pi)

الحلّ

500 sec^{2} (arctan (\frac{1}{2})) (12 π)

الحلّ

7500 π

+1

عشري

23561.94490 \dots

خطوات الحلّ

500 sec^{2} (arctan (\frac{1}{2})) (12 π)

= 500 sec^{2} (arctan (\frac{1}{2})) \cdot 12 π

Rewrite using trig identities:

sec (arctan (\frac{1}{2})) = \frac{5}{2}

sec (arctan (\frac{1}{2}))

Rewrite using trig identities:

sec (arctan (\frac{1}{2})) = 1 + (\frac{1}{2})^{2}

sec (arctan (x)) = 1 + x^{2} :

استخدم المتطابقة التالية

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

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

بسّط

= \frac{5}{2}

= 500 (\frac{5}{2})^{2} \cdot 12 π

500 (\frac{5}{2})^{2} \cdot 12 π

بسّط:

7500 π

500 (\frac{5}{2})^{2} \cdot 12 π

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

(\frac{5}{2})^{2}

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

:فعّل قانون القوى

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

(5)^{2} : 5

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

:فعْل قانون الجذور

= (5^{\frac{1}{2}})^{2}

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

:فعّل قانون القوى

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

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

:اضرب كسور

= \frac{1 \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 1

= 5

= \frac{5}{2 ^{2}}

= 500 \cdot 12 π \frac{5}{2 ^{2}}

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

:اضرب كسور

= \frac{5 \cdot 500 \cdot 12 π}{2 ^{2}}

5 \cdot 500 \cdot 12 = 30000 :

اضرب الأعداد

= \frac{30000 π}{2 ^{2}}

30000

حلل إلى عوامل:

2^{4} \cdot 5^{4} \cdot 3

30000 = 2^{4} \cdot 5^{4} \cdot 3

حلّل إلى عوامل

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

\frac{2 ^{4} \cdot 3 \cdot 5 ^{4} π}{2 ^{2}}

اختزل:

5^{4} \cdot 2^{2} \cdot 3 π

\frac{2 ^{4} \cdot 3 \cdot 5 ^{4} π}{2 ^{2}}

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

:فعّل قانون القوى

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

= 5^{4} \cdot 3 \cdot 2^{4 - 2} π

4 - 2 = 2 :

اطرح الأعداد

= 5^{4} \cdot 2^{2} \cdot 3 π

= 5^{4} \cdot 2^{2} \cdot 3 π

5^{4} = 625

= 2^{2} \cdot 625 \cdot 3 π

2^{2} = 4

= 625 \cdot 4 \cdot 3 π

625 \cdot 4 \cdot 3 = 7500 :

اضرب الأعداد

= 7500 π

= 7500 π

أمثلة شائعة

sin(arccos(5/13))

sin (arccos (\frac{5}{13}))

cos((5pi)/(12))cos(pi/4)+sin((5pi)/(12))sin(pi/4)

cos (\frac{5 π}{12}) cos (\frac{π}{4}) + sin (\frac{5 π}{12}) sin (\frac{π}{4})

sec (- \frac{11 π}{6})

arctan (\frac{13}{9})

\frac{1}{sin ( \frac{π}{2} )}