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شائع >

4.1=4.2cos(18t)+3

الحلّ

4.1 = 4.2 cos (18 t) + 3

الحلّ

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

درجات

t = 4.15649 \dots^{\circ} + 2 0^{\circ} n, t = 15.84350 \dots^{\circ} + 2 0^{\circ} n

خطوات الحلّ

4.1 = 4.2 cos (18 t) + 3

بدّل الأطراف

4.2 cos (18 t) + 3 = 4.1

10

اضرب الطرفين بـ

4.2 cos (18 t) + 3 = 4.1

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

4.2 cos (18 t) \cdot 10 + 3 \cdot 10 = 4.1 \cdot 10

بسّط

42 cos (18 t) + 30 = 41

42 cos (18 t) + 30 = 41

انقل

30

إلى الجانب الأيمن

42 cos (18 t) + 30 = 41

من الطرفين

30

اطرح

42 cos (18 t) + 30 - 30 = 41 - 30

بسّط

42 cos (18 t) = 11

42 cos (18 t) = 11

42

اقسم الطرفين على

42 cos (18 t) = 11

42

اقسم الطرفين على

\frac{42 cos ( 18 t )}{42} = \frac{11}{42}

بسّط

cos (18 t) = \frac{11}{42}

cos (18 t) = \frac{11}{42}

Apply trig inverse properties

cos (18 t) = \frac{11}{42}

cos (18 t) = \frac{11}{42} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

18 t = arccos (\frac{11}{42}) + 2 πn, 18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

18 t = arccos (\frac{11}{42}) + 2 πn, 18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

18 t = arccos (\frac{11}{42}) + 2 πn

حلّ:

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

18 t = arccos (\frac{11}{42}) + 2 πn

18

اقسم الطرفين على

18 t = arccos (\frac{11}{42}) + 2 πn

18

اقسم الطرفين على

\frac{18 t}{18} = \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

بسّط

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

حلّ:

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

18

اقسم الطرفين على

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

18

اقسم الطرفين على

\frac{18 t}{18} = \frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

بسّط

\frac{18 t}{18} = \frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

\frac{18 t}{18}

بسّط:

t

\frac{18 t}{18}

\frac{18}{18} = 1 :

اقسم الأعداد

= t

\frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

بسّط:

\frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

\frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

\frac{2 π}{18}

اختزل:

\frac{π}{9}

\frac{2 π}{18}

2 :

إلغ العوامل المشتركة

= \frac{π}{9}

= \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

\frac{2 πn}{18}

اختزل:

\frac{πn}{9}

\frac{2 πn}{18}

2 :

إلغ العوامل المشتركة

= \frac{πn}{9}

= \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

أظهر الحلّ بالتمثيل العشريّ

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

رسم

أمثلة شائعة

4sin(x)-13=2cos^2(x)-9

4 sin (x) - 13 = 2 cos^{2} (x) - 9

cos(θ)=-8/11

cos (θ) = - \frac{8}{11}

sin(θ)=(sqrt(3))/(12)

sin (θ) = \frac{3}{12}

cos(x)= 12/17

cos (x) = \frac{12}{17}

solvefor x,(d^3+d^2+1)y=cos(3x)solve for

x, (d^{3} + d^{2} + 1) y = cos (3 x)