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tan((8x+1)/5)*cot((x+7)/2)=1

الحلّ

tan (\frac{8 x + 1 ^{\circ}}{5}) \cdot cot (\frac{x + 7 ^{\circ}}{2}) = 1

الحلّ

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}, x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

راديان

x = \frac{π}{60} + \frac{20 π}{11} n, x = \frac{611 π}{660} + \frac{20 π}{11} n

خطوات الحلّ

tan (\frac{8 x + 1 ^{\circ}}{5}) cot (\frac{x + 7 ^{\circ}}{2}) = 1

من الطرفين

1

اطرح

tan (\frac{1440 x + 18 0 ^{\circ}}{900}) cot (\frac{180 x + 126 0 ^{\circ}}{360}) - 1 = 0

sin, cos :

عبّر بواسطة

- 1 + cot (\frac{180 x + 126 0 ^{\circ}}{360}) tan (\frac{18 0 ^{\circ} + 1440 x}{900})

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - 1 + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} tan (\frac{18 0 ^{\circ} + 1440 x}{900})

tan (x) = \frac{sin ( x )}{cos ( x )}

:Use the basic trigonometric identity

= - 1 + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} \cdot \frac{sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

- 1 + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} \cdot \frac{sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

بسّط:

\frac{- sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} ) + cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

- 1 + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} \cdot \frac{sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

\frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} \cdot \frac{sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

اضرب بـ:

\frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{1440 x + 18 0 ^{\circ}}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{1440 x + 18 0 ^{\circ}}{900} )}

\frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} \cdot \frac{sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

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

:اضرب كسور

= \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

= - 1 + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{1440 x + 18 0 ^{\circ}}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{1440 x + 18 0 ^{\circ}}{900} )}

1 = \frac{1 sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

:حوّل الأعداد لكسور

= - \frac{1 \cdot sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )} + \frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- 1 \cdot sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} ) + cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

1 \cdot sin (\frac{180 x + 126 0 ^{\circ}}{360}) = sin (\frac{180 x + 126 0 ^{\circ}}{360}) :

اضرب

= \frac{- sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{1440 x + 18 0 ^{\circ}}{900} ) + cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{1440 x + 18 0 ^{\circ}}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{1440 x + 18 0 ^{\circ}}{900} )}

= \frac{- sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} ) + cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} )}{sin ( \frac{180 x + 126 0 ^{\circ}}{360} ) cos ( \frac{18 0 ^{\circ} + 1440 x}{900} )}

\frac{cos ( \frac{180 x + 126 0 ^{\circ}}{360} ) sin ( \frac{18 0 ^{\circ} + 1440 x}{900} ) - cos ( \frac{18 0 ^{\circ} + 1440 x}{900} ) sin ( \frac{180 x + 126 0 ^{\circ}}{360} )}{cos ( \frac{18 0 ^{\circ} + 1440 x}{900} ) sin ( \frac{180 x + 126 0 ^{\circ}}{360} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (\frac{180 x + 126 0 ^{\circ}}{360}) sin (\frac{18 0 ^{\circ} + 1440 x}{900}) - cos (\frac{18 0 ^{\circ} + 1440 x}{900}) sin (\frac{180 x + 126 0 ^{\circ}}{360}) = 0

Rewrite using trig identities

cos (\frac{180 x + 126 0 ^{\circ}}{360}) sin (\frac{18 0 ^{\circ} + 1440 x}{900}) - cos (\frac{18 0 ^{\circ} + 1440 x}{900}) sin (\frac{180 x + 126 0 ^{\circ}}{360})

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

:فعّل متطابقة الطرح لزوايا

= sin (\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360})

sin (\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360}) = 0

sin (\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360}) = 0 :

حلول عامّة لـ

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{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 0 + 36 0^{\circ} n, \frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 18 0^{\circ} + 36 0^{\circ} n

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 0 + 36 0^{\circ} n, \frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 18 0^{\circ} + 36 0^{\circ} n

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 0 + 36 0^{\circ} n

حلّ:

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 36 0^{\circ} n

اضرب بالمضاعف المشترك الأصغر

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 36 0^{\circ} n

Find Least Common Multiplier of

900, 360 : 1800

900, 360

المضاعف المشترك الأصغر

900

تحليل لعوامل أوّليّة لـ:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

900

900 = 450 \cdot 2, 2

ينقسم على

900

= 2 \cdot 450

450 = 225 \cdot 2, 2

ينقسم على

450

= 2 \cdot 2 \cdot 225

225 = 75 \cdot 3, 3

ينقسم على

225

= 2 \cdot 2 \cdot 3 \cdot 75

75 = 25 \cdot 3, 3

ينقسم على

75

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 25

25 = 5 \cdot 5, 5

ينقسم على

25

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3, 5

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

360

تحليل لعوامل أوّليّة لـ:

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

360

360 = 180 \cdot 2, 2

ينقسم على

360

= 2 \cdot 180

180 = 90 \cdot 2, 2

ينقسم على

180

= 2 \cdot 2 \cdot 90

90 = 45 \cdot 2, 2

ينقسم على

90

= 2 \cdot 2 \cdot 2 \cdot 45

45 = 15 \cdot 3, 3

ينقسم على

45

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 15

15 = 5 \cdot 3, 3

ينقسم على

15

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3, 5

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

360

أو

900

احسب عدد مركّب من عوامل أوّليّة تظهر في

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 = 1800 :

اضرب الأعداد

= 1800

1800 =

اضرب بالمضاعف المشترك الأصغر

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800 - \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800 = 36 0^{\circ} n \cdot 1800

بسّط

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800 - \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800 = 36 0^{\circ} n \cdot 1800

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800

بسّط:

2 (1440 x + 18 0^{\circ})

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800

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

:اضرب كسور

= \frac{( 18 0 ^{\circ} + 1440 x ) \cdot 1800}{900}

\frac{1800}{900} = 2 :

اقسم الأعداد

= 2 (1440 x + 18 0^{\circ})

- \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800

بسّط:

- 5 (180 x + 126 0^{\circ})

- \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800

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

:اضرب كسور

= - \frac{( 180 x + 126 0 ^{\circ} ) \cdot 1800}{360}

\frac{1800}{360} = 5 :

اقسم الأعداد

= - 5 (180 x + 126 0^{\circ})

36 0^{\circ} n \cdot 1800

بسّط:

64800 0^{\circ} n

36 0^{\circ} n \cdot 1800

2 \cdot 1800 = 3600 :

اضرب الأعداد

= 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ})

وسّع:

1980 x - 594 0^{\circ}

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ})

2 (1440 x + 18 0^{\circ})

وسٌع:

2880 x + 36 0^{\circ}

2 (1440 x + 18 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = 2, b = 1440 x, c = 18 0^{\circ}

= 2 \cdot 1440 x + 36 0^{\circ}

2 \cdot 1440 = 2880 :

اضرب الأعداد

= 2880 x + 36 0^{\circ}

= 2880 x + 36 0^{\circ} - 5 (180 x + 126 0^{\circ})

- 5 (180 x + 126 0^{\circ})

وسٌع:

- 900 x - 630 0^{\circ}

- 5 (180 x + 126 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 5, b = 180 x, c = 126 0^{\circ}

= - 5 \cdot 180 x + (- 5) \cdot 126 0^{\circ}

فعّل قوانين سالب-موجب

+ (- a) = - a

= - 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

- 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

بسّط:

- 900 x - 630 0^{\circ}

- 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

5 \cdot 180 = 900 :

اضرب الأعداد

= - 900 x - 5 \cdot 126 0^{\circ}

5 \cdot 7 = 35 :

اضرب الأعداد

= - 900 x - 630 0^{\circ}

= - 900 x - 630 0^{\circ}

= 2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

بسّط:

1980 x - 594 0^{\circ}

2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

جمّع التعابير المتشابهة

= 2880 x - 900 x + 36 0^{\circ} - 630 0^{\circ}

2880 x - 900 x = 1980 x :

اجمع العناصر المتشابهة

= 1980 x + 36 0^{\circ} - 630 0^{\circ}

36 0^{\circ} - 630 0^{\circ} = - 594 0^{\circ} :

اجمع العناصر المتشابهة

= 1980 x - 594 0^{\circ}

= 1980 x - 594 0^{\circ}

1980 x - 594 0^{\circ} = 64800 0^{\circ} n

انقل

594 0^{\circ}

إلى الجانب الأيمن

1980 x - 594 0^{\circ} = 64800 0^{\circ} n

للطرفين

594 0^{\circ}

أضف

1980 x - 594 0^{\circ} + 594 0^{\circ} = 64800 0^{\circ} n + 594 0^{\circ}

بسّط

1980 x = 64800 0^{\circ} n + 594 0^{\circ}

1980 x = 64800 0^{\circ} n + 594 0^{\circ}

1980

اقسم الطرفين على

1980 x = 64800 0^{\circ} n + 594 0^{\circ}

1980

اقسم الطرفين على

\frac{1980 x}{1980} = \frac{64800 0 ^{\circ} n}{1980} + 3^{\circ}

بسّط

\frac{1980 x}{1980} = \frac{64800 0 ^{\circ} n}{1980} + 3^{\circ}

\frac{1980 x}{1980}

بسّط:

x

\frac{1980 x}{1980}

\frac{1980}{1980} = 1 :

اقسم الأعداد

= x

\frac{64800 0 ^{\circ} n}{1980} + 3^{\circ}

بسّط:

\frac{360 0 ^{\circ} n}{11} + 3^{\circ}

\frac{64800 0 ^{\circ} n}{1980} + 3^{\circ}

\frac{64800 0 ^{\circ} n}{1980}

اختزل:

\frac{360 0 ^{\circ} n}{11}

\frac{64800 0 ^{\circ} n}{1980}

180 :

إلغ العوامل المشتركة

= \frac{360 0 ^{\circ} n}{11}

= \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

3^{\circ}

اختزل:

3^{\circ}

3^{\circ}

33 :

إلغ العوامل المشتركة

= 3^{\circ}

= \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 18 0^{\circ} + 36 0^{\circ} n

حلّ:

x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 18 0^{\circ} + 36 0^{\circ} n

اضرب بالمضاعف المشترك الأصغر

\frac{18 0 ^{\circ} + 1440 x}{900} - \frac{180 x + 126 0 ^{\circ}}{360} = 18 0^{\circ} + 36 0^{\circ} n

Find Least Common Multiplier of

900, 360 : 1800

900, 360

المضاعف المشترك الأصغر

900

تحليل لعوامل أوّليّة لـ:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

900

900 = 450 \cdot 2, 2

ينقسم على

900

= 2 \cdot 450

450 = 225 \cdot 2, 2

ينقسم على

450

= 2 \cdot 2 \cdot 225

225 = 75 \cdot 3, 3

ينقسم على

225

= 2 \cdot 2 \cdot 3 \cdot 75

75 = 25 \cdot 3, 3

ينقسم على

75

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 25

25 = 5 \cdot 5, 5

ينقسم على

25

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3, 5

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

360

تحليل لعوامل أوّليّة لـ:

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

360

360 = 180 \cdot 2, 2

ينقسم على

360

= 2 \cdot 180

180 = 90 \cdot 2, 2

ينقسم على

180

= 2 \cdot 2 \cdot 90

90 = 45 \cdot 2, 2

ينقسم على

90

= 2 \cdot 2 \cdot 2 \cdot 45

45 = 15 \cdot 3, 3

ينقسم على

45

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 15

15 = 5 \cdot 3, 3

ينقسم على

15

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

مركّب من أعداد أوّليّة فقط، لذلك تحليل إضافيّ غير ممكن

2, 3, 5

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

360

أو

900

احسب عدد مركّب من عوامل أوّليّة تظهر في

= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 = 1800 :

اضرب الأعداد

= 1800

1800 =

اضرب بالمضاعف المشترك الأصغر

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800 - \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800 = 18 0^{\circ} 1800 + 36 0^{\circ} n \cdot 1800

بسّط

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800 - \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800 = 18 0^{\circ} 1800 + 36 0^{\circ} n \cdot 1800

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800

بسّط:

2 (1440 x + 18 0^{\circ})

\frac{18 0 ^{\circ} + 1440 x}{900} \cdot 1800

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

:اضرب كسور

= \frac{( 18 0 ^{\circ} + 1440 x ) \cdot 1800}{900}

\frac{1800}{900} = 2 :

اقسم الأعداد

= 2 (1440 x + 18 0^{\circ})

- \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800

بسّط:

- 5 (180 x + 126 0^{\circ})

- \frac{180 x + 126 0 ^{\circ}}{360} \cdot 1800

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

:اضرب كسور

= - \frac{( 180 x + 126 0 ^{\circ} ) \cdot 1800}{360}

\frac{1800}{360} = 5 :

اقسم الأعداد

= - 5 (180 x + 126 0^{\circ})

18 0^{\circ} 1800

بسّط:

32400 0^{\circ}

18 0^{\circ} 1800

Apply the commutative law:

18 0^{\circ} 1800 = 32400 0^{\circ}

32400 0^{\circ}

36 0^{\circ} n \cdot 1800

بسّط:

64800 0^{\circ} n

36 0^{\circ} n \cdot 1800

2 \cdot 1800 = 3600 :

اضرب الأعداد

= 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 32400 0^{\circ} + 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 32400 0^{\circ} + 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ}) = 32400 0^{\circ} + 64800 0^{\circ} n

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ})

وسّع:

1980 x - 594 0^{\circ}

2 (1440 x + 18 0^{\circ}) - 5 (180 x + 126 0^{\circ})

2 (1440 x + 18 0^{\circ})

وسٌع:

2880 x + 36 0^{\circ}

2 (1440 x + 18 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = 2, b = 1440 x, c = 18 0^{\circ}

= 2 \cdot 1440 x + 36 0^{\circ}

2 \cdot 1440 = 2880 :

اضرب الأعداد

= 2880 x + 36 0^{\circ}

= 2880 x + 36 0^{\circ} - 5 (180 x + 126 0^{\circ})

- 5 (180 x + 126 0^{\circ})

وسٌع:

- 900 x - 630 0^{\circ}

- 5 (180 x + 126 0^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 5, b = 180 x, c = 126 0^{\circ}

= - 5 \cdot 180 x + (- 5) \cdot 126 0^{\circ}

فعّل قوانين سالب-موجب

+ (- a) = - a

= - 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

- 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

بسّط:

- 900 x - 630 0^{\circ}

- 5 \cdot 180 x - 5 \cdot 126 0^{\circ}

5 \cdot 180 = 900 :

اضرب الأعداد

= - 900 x - 5 \cdot 126 0^{\circ}

5 \cdot 7 = 35 :

اضرب الأعداد

= - 900 x - 630 0^{\circ}

= - 900 x - 630 0^{\circ}

= 2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

بسّط:

1980 x - 594 0^{\circ}

2880 x + 36 0^{\circ} - 900 x - 630 0^{\circ}

جمّع التعابير المتشابهة

= 2880 x - 900 x + 36 0^{\circ} - 630 0^{\circ}

2880 x - 900 x = 1980 x :

اجمع العناصر المتشابهة

= 1980 x + 36 0^{\circ} - 630 0^{\circ}

36 0^{\circ} - 630 0^{\circ} = - 594 0^{\circ} :

اجمع العناصر المتشابهة

= 1980 x - 594 0^{\circ}

= 1980 x - 594 0^{\circ}

1980 x - 594 0^{\circ} = 32400 0^{\circ} + 64800 0^{\circ} n

انقل

594 0^{\circ}

إلى الجانب الأيمن

1980 x - 594 0^{\circ} = 32400 0^{\circ} + 64800 0^{\circ} n

للطرفين

594 0^{\circ}

أضف

1980 x - 594 0^{\circ} + 594 0^{\circ} = 32400 0^{\circ} + 64800 0^{\circ} n + 594 0^{\circ}

بسّط

1980 x = 32994 0^{\circ} + 64800 0^{\circ} n

1980 x = 32994 0^{\circ} + 64800 0^{\circ} n

1980

اقسم الطرفين على

1980 x = 32994 0^{\circ} + 64800 0^{\circ} n

1980

اقسم الطرفين على

\frac{1980 x}{1980} = 166.63636 \dots^{\circ} + \frac{64800 0 ^{\circ} n}{1980}

بسّط

\frac{1980 x}{1980} = 166.63636 \dots^{\circ} + \frac{64800 0 ^{\circ} n}{1980}

\frac{1980 x}{1980}

بسّط:

x

\frac{1980 x}{1980}

\frac{1980}{1980} = 1 :

اقسم الأعداد

= x

166.63636 \dots^{\circ} + \frac{64800 0 ^{\circ} n}{1980}

بسّط:

166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

166.63636 \dots^{\circ} + \frac{64800 0 ^{\circ} n}{1980}

166.63636 \dots^{\circ}

اختزل:

166.63636 \dots^{\circ}

166.63636 \dots^{\circ}

3 :

إلغ العوامل المشتركة

= 166.63636 \dots^{\circ}

= 166.63636 \dots^{\circ} + \frac{64800 0 ^{\circ} n}{1980}

\frac{64800 0 ^{\circ} n}{1980}

اختزل:

\frac{360 0 ^{\circ} n}{11}

\frac{64800 0 ^{\circ} n}{1980}

180 :

إلغ العوامل المشتركة

= \frac{360 0 ^{\circ} n}{11}

= 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

x = \frac{360 0 ^{\circ} n}{11} + 3^{\circ}, x = 166.63636 \dots^{\circ} + \frac{360 0 ^{\circ} n}{11}

أمثلة شائعة

sin(4t)cos(t)=sin(t)cos(4t)

sin (4 t) cos (t) = sin (t) cos (4 t)

sqrt(3)tan(3x+pi/2)+1=0

3 tan (3 x + \frac{π}{2}) + 1 = 0

-2sin(x)-2cos(x)=0

- 2 sin (x) - 2 cos (x) = 0

7sin(b)=5sin(70)

7 sin (b) = 5 sin (7 0^{\circ})

5sin(x)+2cos^2(x)=4

5 sin (x) + 2 cos^{2} (x) = 4