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sec((13pi)/(12))

الحلّ

sec (\frac{13 π}{12})

الحلّ

2 (1 - 3)

العشري

- 1.03527 \dots

خطوات الحلّ

sec (\frac{13 π}{12})

Rewrite using trig identities:

\frac{1}{cos ( \frac{13 π}{12} )}

sec (\frac{13 π}{12})

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

= \frac{1}{cos ( \frac{13 π}{12} )}

= \frac{1}{cos ( \frac{13 π}{12} )}

Rewrite using trig identities:

cos (\frac{13 π}{12}) = \frac{2 ( - 3 - 1 )}{4}

cos (\frac{13 π}{12})

Rewrite using trig identities:

cos (\frac{5 π}{6}) cos (\frac{π}{4}) - sin (\frac{5 π}{6}) sin (\frac{π}{4})

cos (\frac{13 π}{12})

cos (\frac{5 π}{6} + \frac{π}{4})

كـ

cos (\frac{13 π}{12})

أكتب

= cos (\frac{5 π}{6} + \frac{π}{4})

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

:فعّل متطابقة الجمع لزوايا

= cos (\frac{5 π}{6}) cos (\frac{π}{4}) - sin (\frac{5 π}{6}) sin (\frac{π}{4})

= cos (\frac{5 π}{6}) cos (\frac{π}{4}) - sin (\frac{5 π}{6}) sin (\frac{π}{4})

استخدم المتطابقة الأساسيّة التالية:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

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{3}{2}

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}

استخدم المتطابقة الأساسيّة التالية:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 π}{6})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} 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}

استخدم المتطابقة الأساسيّة التالية:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= (- \frac{3}{2}) \frac{2}{2} - \frac{1}{2} \cdot \frac{2}{2}

(- \frac{3}{2}) \frac{2}{2} - \frac{1}{2} \cdot \frac{2}{2}

بسّط:

\frac{2 ( - 3 - 1 )}{4}

(- \frac{3}{2}) \frac{2}{2} - \frac{1}{2} \cdot \frac{2}{2}

(- a) = - a

:احذف الأقواس

= - \frac{3}{2} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{2}{2}

\frac{2}{2}

قم باخراج العامل المشترك

= \frac{2}{2} (- \frac{3}{2} - \frac{1}{2})

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

- \frac{3}{2} - \frac{1}{2}

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

فعّل القانون

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

= \frac{2}{2} \cdot \frac{- 1 - 3}{2}

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

:اضرب كسور

= \frac{( - 3 - 1 ) 2}{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2 ( - 1 - 3 )}{4}

= \frac{2 ( - 3 - 1 )}{4}

= \frac{1}{\frac{2 ( - 3 - 1 )}{4}}

\frac{1}{\frac{2 ( - 3 - 1 )}{4}}

بسّط:

2 (1 - 3)

\frac{1}{\frac{2 ( - 3 - 1 )}{4}}

\frac{1}{\frac{b}{c}} = \frac{c}{b}

: استخدم ميزات الكسور التالية

= \frac{4}{2 ( - 3 - 1 )}

4

حلل إلى عوامل:

2^{2}

4 = 2^{2}

حلّل إلى عوامل

= \frac{2 ^{2}}{2 ( - 1 - 3 )}

\frac{2 ^{2}}{2 ( - 3 - 1 )}

اختزل:

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

\frac{2 ^{2}}{2 ( - 3 - 1 )}

:فعْل قانون الجذور

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

= \frac{2 ^{2}}{2 ^{\frac{1}{2}} ( - 1 - 3 )}

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

:فعّل قانون القوى

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

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

2 - \frac{1}{2} = \frac{3}{2} :

اطرح الأعداد

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

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

2^{\frac{3}{2}} = 22

2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2^{1 + \frac{1}{2}}

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

x^{a + b} = x^{a} x^{b}

:فعّل قانون القوى

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

بسّط

= 22

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

\frac{2 2}{- 3 - 1}

حوّل لصيغة عدد كسريّ:

2 (1 - 3)

\frac{2 2}{- 3 - 1}

\frac{- 3 + 1}{- 3 + 1}

اضرب بالمرافق

= \frac{2 2 ( - 3 + 1 )}{( - 3 - 1 ) ( - 3 + 1 )}

(- 3 - 1) (- 3 + 1) = 2

(- 3 - 1) (- 3 + 1)

(a + b) (c + d) = a c + a d + b c + b d

(a + b) (c + d) = a c + a d + b c + b d

فعّل قانون التوزيع

a = - 3, b = - 1, c = - 3, d = 1

= (- 3) (- 3) + (- 3) \cdot 1 + (- 1) (- 3) + (- 1) \cdot 1

فعّل قوانين سالب-موجب

(- a) (- b) = ab, + (- a) = - a

= 33 - 1 \cdot 3 + 1 \cdot 3 - 1 \cdot 1

33 - 1 \cdot 3 + 1 \cdot 3 - 1 \cdot 1

بسّط:

2

33 - 1 \cdot 3 + 1 \cdot 3 - 1 \cdot 1

- 1 \cdot 3 + 1 \cdot 3 = 0 :

اجمع العناصر المتشابهة

= 33 - 1 \cdot 1

a a = a

:فعْل قانون الجذور

33 = 3

= 3 - 1 \cdot 1

1 \cdot 1 = 1 :

اضرب الأعداد

= 3 - 1

3 - 1 = 2 :

اطرح الأعداد

= 2

= 2

= \frac{2 2 ( - 3 + 1 )}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= 2 (1 - 3)

= 2 (1 - 3)

= 2 (1 - 3)

أمثلة شائعة

arcsin(1.17)

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tan((7pi)/6-pi/4)

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cos(45/2)

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cot(24)

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