ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

cos(3x)=(sqrt(3))/3

الحلّ

cos (3 x) = \frac{3}{3}

الحلّ

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

+1

درجات

x = 18.24520 \dots^{\circ} + 12 0^{\circ} n, x = 101.75479 \dots^{\circ} + 12 0^{\circ} n

خطوات الحلّ

cos (3 x) = \frac{3}{3}

Apply trig inverse properties

cos (3 x) = \frac{3}{3}

cos (3 x) = \frac{3}{3} :

حلول عامّة لـ

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

3 x = arccos (\frac{3}{3}) + 2 πn, 3 x = 2 π - arccos (\frac{3}{3}) + 2 πn

3 x = arccos (\frac{3}{3}) + 2 πn, 3 x = 2 π - arccos (\frac{3}{3}) + 2 πn

3 x = arccos (\frac{3}{3}) + 2 πn

حلّ:

x = \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{3}{3}) + 2 πn

arccos (\frac{3}{3}) + 2 πn

بسّط:

arccos (\frac{1}{3}) + 2 πn

arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

3 = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{3}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

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

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

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{1}{3 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

3^{\frac{1}{2}} = 3

= \frac{1}{3}

= arccos (\frac{1}{3}) + 2 πn

3 x = arccos (\frac{1}{3}) + 2 πn

3

اقسم الطرفين على

3 x = arccos (\frac{1}{3}) + 2 πn

3

اقسم الطرفين على

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

بسّط

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

\frac{3 x}{3}

بسّط:

x

\frac{3 x}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= x

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

بسّط:

\frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

= \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{3}{3}) + 2 πn

حلّ:

x = \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{3}{3}) + 2 πn

2 π - arccos (\frac{3}{3}) + 2 πn

بسّط:

2 π - arccos (\frac{1}{3}) + 2 πn

2 π - arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

3 = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{3}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

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

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

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{1}{3 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

3^{\frac{1}{2}} = 3

= \frac{1}{3}

= 2 π - arccos (\frac{1}{3}) + 2 πn

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

3

اقسم الطرفين على

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

3

اقسم الطرفين على

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

بسّط

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

\frac{3 x}{3}

بسّط:

x

\frac{3 x}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= x

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

بسّط:

\frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

= \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

رسم

أمثلة شائعة

-6csc^2(x)+cot(x)=-18

- 6 csc^{2} (x) + cot (x) = - 18

tan (θ) = \frac{7}{7}

tan (2 x) = 0.75

3tan^2(x)+7tan(x)+4=0

3 tan^{2} (x) + 7 tan (x) + 4 = 0

cos(2θ)-3=-5sin(θ)

cos (2 θ) - 3 = - 5 sin (θ)