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شائع >

cos(-(11pi)/(12))

الحلّ

cos (- \frac{11 π}{12})

الحلّ

\frac{- 6 - 2}{4}

العشري

- 0.96592 \dots

خطوات الحلّ

cos (- \frac{11 π}{12})

cos (- x) = cos (x) :

استخدم القانون التالي

cos (- \frac{11 π}{12}) = cos (\frac{11 π}{12})

= cos (\frac{11 π}{12})

Rewrite using trig identities:

cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

cos (\frac{11 π}{12})

cos (\frac{3 π}{4} + \frac{π}{6})

كـ

cos (\frac{11 π}{12})

أكتب

= cos (\frac{3 π}{4} + \frac{π}{6})

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

:فعّل متطابقة الجمع لزوايا

= cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

= cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

استخدم المتطابقة الأساسيّة التالية:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 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:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{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:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 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}

استخدم المتطابقة الأساسيّة التالية:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{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}

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

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

بسّط:

\frac{- 6 - 2}{4}

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

(- a) = - a

:احذف الأقواس

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

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

\frac{2}{2} \cdot \frac{3}{2}

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

:اضرب كسور

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

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2 3}{4}

23

بسّط:

6

23

a b = a \cdot b

:فعْل قانون الجذور

23 = 2 \cdot 3

= 2 \cdot 3

2 \cdot 3 = 6 :

اضرب الأعداد

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

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

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

:اضرب كسور

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

2 \cdot 1 = 2 :

اضرب

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

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2}{4}

= - \frac{6}{4} - \frac{2}{4}

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

فعّل القانون

= \frac{- 6 - 2}{4}

= \frac{- 6 - 2}{4}

أمثلة شائعة

arctan((4sqrt(3))/4)

arctan (\frac{4 3}{4})

sec((13pi)/4)

sec (\frac{13 π}{4})

sinh(pi/2)

sinh (\frac{π}{2})

cos^5(pi)

cos^{5} (π)

cot(3)

cot (3)