ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

sin^5(3x^2+2)=0.35

الحلّ

sin^{5} (3 x^{2} + 2) = 0.35

الحلّ

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

+1

درجات

x = 0^{\circ} + 75.63899 \dots^{\circ} n, x = 0^{\circ} - 75.63899 \dots^{\circ} n, x = 0^{\circ} + 84.20452 \dots^{\circ} n, x = 0^{\circ} - 84.20452 \dots^{\circ} n

خطوات الحلّ

sin^{5} (3 x^{2} + 2) = 0.35

x = n f (a)

فرديّ، الحلّ هو

n, x^{n} = f (a)

لـ

sin (3 x^{2} + 2) = 5 0.35

Apply trig inverse properties

sin (3 x^{2} + 2) = 5 0.35

sin (3 x^{2} + 2) = 5 0.35 :

حلول عامّة لـ

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

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn, 3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

حلّ:

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

انقل

2

إلى الجانب الأيمن

3 x^{2} + 2 = arcsin (5 0.35) + 2 πn

من الطرفين

2

اطرح

3 x^{2} + 2 - 2 = arcsin (5 0.35) + 2 πn - 2

بسّط

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

3

اقسم الطرفين على

3 x^{2} = arcsin (5 0.35) + 2 πn - 2

3

اقسم الطرفين على

\frac{3 x ^{2}}{3} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x = f (a), - f (a)

الحلول هي

x^{2} = f (a)

لـ

x = \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط:

\frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

وحّد الكسور:

\frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

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

فعّل القانون

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط:

- \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

وحّد الكسور:

\frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

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

فعّل القانون

= \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{2 πn + arcsin ( 5 0.35 ) - 2}{3}

= - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

حلّ:

x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

انقل

2

إلى الجانب الأيمن

3 x^{2} + 2 = π - arcsin (5 0.35) + 2 πn

من الطرفين

2

اطرح

3 x^{2} + 2 - 2 = π - arcsin (5 0.35) + 2 πn - 2

بسّط

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

3

اقسم الطرفين على

3 x^{2} = π - arcsin (5 0.35) + 2 πn - 2

3

اقسم الطرفين على

\frac{3 x ^{2}}{3} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x^{2} = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

x = f (a), - f (a)

الحلول هي

x^{2} = f (a)

لـ

x = \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}, x = - \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط:

\frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

وحّد الكسور:

\frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

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

فعّل القانون

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

بسّط:

- \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

- \frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

\frac{π}{3} - \frac{arcsin ( 5 0.35 )}{3} + \frac{2 πn}{3} - \frac{2}{3}

وحّد الكسور:

\frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

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

فعّل القانون

= \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

= - \frac{π + 2 πn - 2 - arcsin ( 5 0.35 )}{3}

= - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

x = \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}, x = - \frac{π - arcsin ( 5 0.35 ) + 2 πn - 2}{3}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{0.94519 \dots + 2 πn - 2}{3}, x = - \frac{0.94519 \dots + 2 πn - 2}{3}, x = \frac{π - 0.94519 \dots + 2 πn - 2}{3}, x = - \frac{π - 0.94519 \dots + 2 πn - 2}{3}

رسم

أمثلة شائعة

cos(θ)-sin(-θ)=0

cos (θ) - sin (- θ) = 0

cos^{2} (3 x) = \frac{1}{4}

cos(7x-30)sec(x)=1

cos (7 x - 30) sec (x) = 1

sin (θ) = \frac{45}{53}

2-sin^2(θ)+2sin(θ)=0

2 - sin^{2} (θ) + 2 sin (θ) = 0