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solvefor x,-sin(0.6(x+y))*0.6+0.25=0

الحلّ

solve for

x, - sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

الحلّ

x = \frac{0.42977 \dots + 2 πn}{0.6} - y, x = \frac{π - 0.42977 \dots + 2 πn}{0.6} - y

خطوات الحلّ

- sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

100

اضرب الطرفين بـ

- sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- sin (0.6 (x + y)) \cdot 0.6 \cdot 100 + 0.25 \cdot 100 = 0 \cdot 100

بسّط

- 60 sin (0.6 (x + y)) + 25 = 0

- 60 sin (0.6 (x + y)) + 25 = 0

انقل

25

إلى الجانب الأيمن

- 60 sin (0.6 (x + y)) + 25 = 0

من الطرفين

25

اطرح

- 60 sin (0.6 (x + y)) + 25 - 25 = 0 - 25

بسّط

- 60 sin (0.6 (x + y)) = - 25

- 60 sin (0.6 (x + y)) = - 25

- 60

اقسم الطرفين على

- 60 sin (0.6 (x + y)) = - 25

- 60

اقسم الطرفين على

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60} = \frac{- 25}{- 60}

بسّط

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60} = \frac{- 25}{- 60}

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60}

بسّط:

sin (0.6 (x + y))

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60}

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

: استخدم ميزات الكسور التالية

= \frac{60 sin ( 0.6 ( x + y ) )}{60}

\frac{60}{60} = 1 :

اقسم الأعداد

= sin (0.6 (x + y))

\frac{- 25}{- 60}

بسّط:

\frac{5}{12}

\frac{- 25}{- 60}

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

: استخدم ميزات الكسور التالية

= \frac{25}{60}

5 :

إلغ العوامل المشتركة

= \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

Apply trig inverse properties

sin (0.6 (x + y)) = \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn, 0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn, 0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn

حلّ:

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn

0.6

اقسم الطرفين على

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn

0.6

اقسم الطرفين على

\frac{0.6 ( x + y )}{0.6} = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

بسّط

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

انقل

y

إلى الجانب الأيمن

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

من الطرفين

y

اطرح

x + y - y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

بسّط

x + y - y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

x + y - y

بسّط:

x

x + y - y

y - y = 0 :

اجمع العناصر المتشابهة

= x

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

بسّط:

\frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

وحّد الكسور:

\frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

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

فعّل القانون

= \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

= \frac{2 πn + arcsin ( \frac{5}{12} )}{0.6} - y

= \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

حلّ:

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

0.6

اقسم الطرفين على

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

0.6

اقسم الطرفين على

\frac{0.6 ( x + y )}{0.6} = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

بسّط

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

انقل

y

إلى الجانب الأيمن

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

من الطرفين

y

اطرح

x + y - y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

بسّط

x + y - y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

x + y - y

بسّط:

x

x + y - y

y - y = 0 :

اجمع العناصر المتشابهة

= x

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

بسّط:

\frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

وحّد الكسور:

\frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

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

فعّل القانون

= \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

= \frac{π + 2 πn - arcsin ( \frac{5}{12} )}{0.6} - y

= \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y, x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

أظهر الحلّ بالتمثيل العشريّ

x = \frac{0.42977 \dots + 2 πn}{0.6} - y, x = \frac{π - 0.42977 \dots + 2 πn}{0.6} - y

أمثلة شائعة

5sin(60t)=0

5 sin (60 t) = 0

18sin^2(x)+3cos(x)-17=0

18 sin^{2} (x) + 3 cos (x) - 17 = 0

sin(2θ)=0.4905

sin (2 θ) = 0.4905

tan(θ)=(-4.86)/(14.56)

tan (θ) = \frac{- 4.86}{14.56}

12cos(x)+5sin(x)=3

12 cos (x) + 5 sin (x) = 3