English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

sin(62.8x+pi/4)=sin(pi/4)

الحلّ

sin (62.8 x + \frac{π}{4}) = sin (\frac{π}{4})

الحلّ

x = \frac{5 πn}{157}, x = \frac{5 πn}{157} + \frac{5 π}{628}

درجات

x = 0^{\circ} + 5.73248 \dots^{\circ} n, x = 1.43312 \dots^{\circ} + 5.73248 \dots^{\circ} n

خطوات الحلّ

sin (62.8 x + \frac{π}{4}) = sin (\frac{π}{4})

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

sin (62.8 x + \frac{π}{4}) = \frac{2}{2}

sin (62.8 x + \frac{π}{4}) = \frac{2}{2} :

حلول عامّة لـ

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}

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn, 62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn, 62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn

حلّ:

x = \frac{5 πn}{157}

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn

من الطرفين

\frac{π}{4}

اطرح

62.8 x + \frac{π}{4} - \frac{π}{4} = \frac{π}{4} + 2 πn - \frac{π}{4}

بسّط

62.8 x = 2 πn

10

اضرب الطرفين بـ

62.8 x = 2 πn

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

62.8 x \cdot 10 = 2 πn \cdot 10

بسّط

628 x = 20 πn

628 x = 20 πn

628

اقسم الطرفين على

628 x = 20 πn

628

اقسم الطرفين على

\frac{628 x}{628} = \frac{20 πn}{628}

بسّط

x = \frac{5 πn}{157}

x = \frac{5 πn}{157}

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

حلّ:

x = \frac{5 πn}{157} + \frac{5 π}{628}

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

10

اضرب الطرفين بـ

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

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

62.8 x \cdot 10 + \frac{π}{4} \cdot 10 = \frac{3 π}{4} \cdot 10 + 2 πn \cdot 10

بسّط

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

انقل

\frac{5 π}{2}

إلى الجانب الأيمن

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

من الطرفين

\frac{5 π}{2}

اطرح

628 x + \frac{5 π}{2} - \frac{5 π}{2} = \frac{15 π}{2} + 20 πn - \frac{5 π}{2}

بسّط

628 x + \frac{5 π}{2} - \frac{5 π}{2} = \frac{15 π}{2} + 20 πn - \frac{5 π}{2}

628 x + \frac{5 π}{2} - \frac{5 π}{2}

بسّط:

628 x

628 x + \frac{5 π}{2} - \frac{5 π}{2}

\frac{5 π}{2} - \frac{5 π}{2} = 0 :

اجمع العناصر المتشابهة

= 628 x

\frac{15 π}{2} + 20 πn - \frac{5 π}{2}

بسّط:

20 πn + 5 π

\frac{15 π}{2} + 20 πn - \frac{5 π}{2}

جمّع التعابير المتشابهة

= 20 πn - \frac{5 π}{2} + \frac{15 π}{2}

- \frac{5 π}{2} + \frac{15 π}{2}

وحّد الكسور:

5 π

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

فعّل القانون

= \frac{- 5 π + 15 π}{2}

- 5 π + 15 π = 10 π :

اجمع العناصر المتشابهة

= \frac{10 π}{2}

\frac{10}{2} = 5 :

اقسم الأعداد

= 5 π

= 20 πn + 5 π

628 x = 20 πn + 5 π

628 x = 20 πn + 5 π

628 x = 20 πn + 5 π

628

اقسم الطرفين على

628 x = 20 πn + 5 π

628

اقسم الطرفين على

\frac{628 x}{628} = \frac{20 πn}{628} + \frac{5 π}{628}

بسّط

x = \frac{5 πn}{157} + \frac{5 π}{628}

x = \frac{5 πn}{157} + \frac{5 π}{628}

x = \frac{5 πn}{157}, x = \frac{5 πn}{157} + \frac{5 π}{628}

رسم

أمثلة شائعة

4cos^{(2)}(x)-4cos(x)+1=0

4 cos^{(2)} (x) - 4 cos (x) + 1 = 0

3cos(2x)=3sin(x)

3 cos (2 x) = 3 sin (x)

4cos(θ/2)+3=-2cos(θ)

4 cos (\frac{θ}{2}) + 3 = - 2 cos (θ)

8cos(2x)-1=2

8 cos (2 x) - 1 = 2

2cos(2x)+sqrt(3)=2sqrt(3)

2 cos (2 x) + 3 = 23