English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

0.08=0.12cos^2(3.922t)

الحلّ

0.08 = 0.12 cos^{2} (3.922 t)

الحلّ

t = \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}, t = - \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}

درجات

t = 8.99143 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 82.79847 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 36.90352 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = - 36.90352 \dots^{\circ} + 91.78990 \dots^{\circ} n

خطوات الحلّ

0.08 = 0.12 cos^{2} (3.922 t)

بدّل الأطراف

0.12 cos^{2} (3.922 t) = 0.08

بالاستعانة بطريقة التعويض

0.12 cos^{2} (3.922 t) = 0.08

cos (3.922 t) = u :

على افتراض أنّ

0.12 u^{2} = 0.08

0.12 u^{2} = 0.08 : u = \frac{2}{3}, u = - \frac{2}{3}

0.12 u^{2} = 0.08

100

اضرب الطرفين بـ

0.12 u^{2} = 0.08

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

0.12 u^{2} \cdot 100 = 0.08 \cdot 100

بسّط

12 u^{2} = 8

12 u^{2} = 8

12

اقسم الطرفين على

12 u^{2} = 8

12

اقسم الطرفين على

\frac{12 u ^{2}}{12} = \frac{8}{12}

بسّط

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

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

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

الحلول هي

x^{2} = f (a)

لـ

u = \frac{2}{3}, u = - \frac{2}{3}

u = cos (3.922 t)

استبدل مجددًا

cos (3.922 t) = \frac{2}{3}, cos (3.922 t) = - \frac{2}{3}

cos (3.922 t) = \frac{2}{3}, cos (3.922 t) = - \frac{2}{3}

cos (3.922 t) = \frac{2}{3} : t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = \frac{2}{3}

Apply trig inverse properties

cos (3.922 t) = \frac{2}{3}

cos (3.922 t) = \frac{2}{3} :

حلول عامّة لـ

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

3.922 t = arccos (\frac{2}{3}) + 2 πn, 3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

3.922 t = arccos (\frac{2}{3}) + 2 πn, 3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

3.922 t = arccos (\frac{2}{3}) + 2 πn

حلّ:

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = arccos (\frac{2}{3}) + 2 πn

3.922

اقسم الطرفين على

3.922 t = arccos (\frac{2}{3}) + 2 πn

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

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

حلّ:

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

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

3.922

اقسم الطرفين على

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

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = - \frac{2}{3} : t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = - \frac{2}{3}

Apply trig inverse properties

cos (3.922 t) = - \frac{2}{3}

cos (3.922 t) = - \frac{2}{3} :

حلول عامّة لـ

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

3.922 t = arccos (- \frac{2}{3}) + 2 πn, 3.922 t = - arccos (- \frac{2}{3}) + 2 πn

3.922 t = arccos (- \frac{2}{3}) + 2 πn, 3.922 t = - arccos (- \frac{2}{3}) + 2 πn

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

حلّ:

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

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

3.922

اقسم الطرفين على

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

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

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

حلّ:

t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

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

3.922

اقسم الطرفين على

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

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

وحّد الحلول

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

أظهر الحلّ بالتمثيل العشريّ

t = \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}, t = - \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}

رسم

أمثلة شائعة

(15)/(sin(32))=(12)/(sin(b))

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

(sin(x))/(25)=(sin(125))/(165.6)

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

2cos(3θ)-1=0

2 cos (3 θ) - 1 = 0

cos(4x)=cos(8x)

cos (4 x) = cos (8 x)

cos(2x)-cos(x)=2

cos (2 x) - cos (x) = 2