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2cos(2x)= 1/2

الحلّ

2 cos (2 x) = \frac{1}{2}

الحلّ

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

+1

درجات

x = 37.76124 \dots^{\circ} + 18 0^{\circ} n, x = 142.23875 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

2 cos (2 x) = \frac{1}{2}

2

اقسم الطرفين على

2 cos (2 x) = \frac{1}{2}

2

اقسم الطرفين على

\frac{2 cos ( 2 x )}{2} = \frac{\frac{1}{2}}{2}

بسّط

\frac{2 cos ( 2 x )}{2} = \frac{\frac{1}{2}}{2}

\frac{2 cos ( 2 x )}{2}

بسّط:

cos (2 x)

\frac{2 cos ( 2 x )}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= cos (2 x)

\frac{\frac{1}{2}}{2}

بسّط:

\frac{1}{4}

\frac{\frac{1}{2}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{1}{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{1}{4}

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

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

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

Apply trig inverse properties

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

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

حلول عامّة لـ

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

2 x = arccos (\frac{1}{4}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

2 x = arccos (\frac{1}{4}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

2 x = arccos (\frac{1}{4}) + 2 πn

حلّ:

x = \frac{arccos ( \frac{1}{4} )}{2} + πn

2 x = arccos (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

2 x = arccos (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

\frac{2 x}{2} = \frac{arccos ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

بسّط

x = \frac{arccos ( \frac{1}{4} )}{2} + πn

x = \frac{arccos ( \frac{1}{4} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

حلّ:

x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

بسّط

x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

x = \frac{arccos ( \frac{1}{4} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

أظهر الحلّ بالتمثيل العشريّ

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

أمثلة شائعة

(sin(73))/(34)=(sin(d))/(29)

\frac{sin ( 7 3 ^{\circ} )}{34} = \frac{sin ( d )}{29}

solvefor θ,(90^2)/(250(32.2))=tan(θ)solve for

θ, \frac{9 0 ^{2}}{250 ( 32.2 )} = tan (θ)

sin(θ)=2sin(θ)cos(θ)

sin (θ) = 2 sin (θ) cos (θ)

solvefor x,arccos(e^{-x})= pi/3 solve for

x, arccos (e^{- x}) = \frac{π}{3}

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