ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع >

1-1/2*cos(3θ)=(4-sqrt(2))/4 ,0<= θ<= 360

الحلّ

1 - \frac{1}{2} \cdot cos (3 θ) = \frac{4 - 2}{4}, 0^{\circ} \leq θ \leq 36 0^{\circ}

الحلّ

θ = 1 5^{\circ}, θ = 10 5^{\circ}, θ = 13 5^{\circ}, θ = 22 5^{\circ}, θ = 25 5^{\circ}, θ = 34 5^{\circ}

+1

راديان

θ = \frac{π}{12}, θ = \frac{7 π}{12}, θ = \frac{3 π}{4}, θ = \frac{5 π}{4}, θ = \frac{17 π}{12}, θ = \frac{23 π}{12}

خطوات الحلّ

1 - \frac{1}{2} cos (3 θ) = \frac{4 - 2}{4}, 0^{\circ} \leq θ \leq 36 0^{\circ}

انقل

1

إلى الجانب الأيمن

1 - \frac{1}{2} cos (3 θ) = \frac{4 - 2}{4}

من الطرفين

1

اطرح

1 - \frac{1}{2} cos (3 θ) - 1 = \frac{4 - 2}{4} - 1

بسّط

- \frac{1}{2} cos (3 θ) = \frac{4 - 2}{4} - 1

- \frac{1}{2} cos (3 θ) = \frac{4 - 2}{4} - 1

- 2

اضرب الطرفين بـ

- \frac{1}{2} cos (3 θ) = \frac{4 - 2}{4} - 1

- 2

اضرب الطرفين بـ

(- \frac{1}{2} cos (3 θ)) (- 2) = \frac{4 - 2}{4} (- 2) - 1 \cdot (- 2)

بسّط

(- \frac{1}{2} cos (3 θ)) (- 2) = \frac{4 - 2}{4} (- 2) - 1 \cdot (- 2)

(- \frac{1}{2} cos (3 θ)) (- 2)

بسّط:

cos (3 θ)

(- \frac{1}{2} cos (3 θ)) (- 2)

(- a) = - a, - (- a) = a

:احذف الأقواس

= \frac{1}{2} cos (3 θ) \cdot 2

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

:اضرب كسور

= \frac{1 \cdot 2}{2} cos (3 θ)

2 :

إلغ العوامل المشتركة

= cos (3 θ) \cdot 1

cos (3 θ) \cdot 1 = cos (3 θ) :

اضرب

= cos (3 θ)

\frac{4 - 2}{4} (- 2) - 1 \cdot (- 2)

بسّط:

- \frac{4 - 2}{2} + 2

\frac{4 - 2}{4} (- 2) - 1 \cdot (- 2)

(- a) = - a, - (- a) = a

:احذف الأقواس

= - \frac{4 - 2}{4} \cdot 2 + 1 \cdot 2

\frac{4 - 2}{4} \cdot 2 = \frac{4 - 2}{2}

\frac{4 - 2}{4} \cdot 2

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

:اضرب كسور

= \frac{( 4 - 2 ) \cdot 2}{4}

2 :

إلغ العوامل المشتركة

= \frac{4 - 2}{2}

1 \cdot 2 = 2

1 \cdot 2

1 \cdot 2 = 2 :

اضرب الأعداد

= 2

= - \frac{4 - 2}{2} + 2

cos (3 θ) = - \frac{4 - 2}{2} + 2

cos (3 θ) = - \frac{4 - 2}{2} + 2

cos (3 θ) = - \frac{4 - 2}{2} + 2

Apply trig inverse properties

cos (3 θ) = - \frac{4 - 2}{2} + 2

cos (3 θ) = - \frac{4 - 2}{2} + 2 :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

3 θ = arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n, 3 θ = 36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

3 θ = arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n, 3 θ = 36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

3 θ = arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

حلّ:

θ = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

3 θ = arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

بسّط:

4 5^{\circ} + 36 0^{\circ} n

arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

استخدم المتطابقة الأساسيّة التالية:

arccos (- \frac{4 - 2}{2} + 2) = 4 5^{\circ}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 4 5^{\circ} + 36 0^{\circ} n

3 θ = 4 5^{\circ} + 36 0^{\circ} n

3

اقسم الطرفين على

3 θ = 4 5^{\circ} + 36 0^{\circ} n

3

اقسم الطرفين على

\frac{3 θ}{3} = \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

بسّط

\frac{3 θ}{3} = \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{3 θ}{3}

بسّط:

θ

\frac{3 θ}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= θ

\frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

بسّط:

1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

\frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{4 5 ^{\circ}}{3} = 1 5^{\circ}

\frac{4 5 ^{\circ}}{3}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{4 \cdot 3}

4 \cdot 3 = 12 :

اضرب الأعداد

= 1 5^{\circ}

= 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

3 θ = 36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

حلّ:

θ = 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

3 θ = 36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

بسّط:

36 0^{\circ} - 4 5^{\circ} + 36 0^{\circ} n

36 0^{\circ} - arccos (- \frac{4 - 2}{2} + 2) + 36 0^{\circ} n

استخدم المتطابقة الأساسيّة التالية:

arccos (- \frac{4 - 2}{2} + 2) = 4 5^{\circ}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 36 0^{\circ} - 4 5^{\circ} + 36 0^{\circ} n

3 θ = 36 0^{\circ} - 4 5^{\circ} + 36 0^{\circ} n

3

اقسم الطرفين على

3 θ = 36 0^{\circ} - 4 5^{\circ} + 36 0^{\circ} n

3

اقسم الطرفين على

\frac{3 θ}{3} = 12 0^{\circ} - \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

بسّط

\frac{3 θ}{3} = 12 0^{\circ} - \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{3 θ}{3}

بسّط:

θ

\frac{3 θ}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= θ

12 0^{\circ} - \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

بسّط:

12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

12 0^{\circ} - \frac{4 5 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{4 5 ^{\circ}}{3} = 1 5^{\circ}

\frac{4 5 ^{\circ}}{3}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{4 \cdot 3}

4 \cdot 3 = 12 :

اضرب الأعداد

= 1 5^{\circ}

= 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

θ = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}, θ = 12 0^{\circ} - 1 5^{\circ} + \frac{36 0 ^{\circ} n}{3}

0 \leq θ \leq 36 0^{\circ} :

حلول للمدى

θ = 1 5^{\circ}, θ = 10 5^{\circ}, θ = 13 5^{\circ}, θ = 22 5^{\circ}, θ = 25 5^{\circ}, θ = 34 5^{\circ}

رسم

أمثلة شائعة

(cos(x))/(sin(x))=-0.00836

\frac{cos ( x )}{sin ( x )} = - 0.00836

sin^3(x)=cos^3(x)

sin^{3} (x) = cos^{3} (x)

2sin(θ)=3cos(θ)-1,0<,θ<360

2 sin (θ) = 3 cos (θ) - 1, 0 <, θ < 360

cot(2θ)+csc(2θ)-7=0

cot (2 θ) + csc (2 θ) - 7 = 0

sec(x)sin(x)+cos(x)=sec(x)

sec (x) sin (x) + cos (x) = sec (x)