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شائع علم المثلثات >

6sin(2x-30)+2=0

الحلّ

6 sin (2 x - 3 0^{\circ}) + 2 = 0

الحلّ

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

راديان

x = \frac{π}{12} - \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} + \frac{π}{12} + \frac{0.33983 \dots}{2} + πn

خطوات الحلّ

6 sin (2 x - 3 0^{\circ}) + 2 = 0

انقل

2

إلى الجانب الأيمن

6 sin (2 x - 3 0^{\circ}) + 2 = 0

من الطرفين

2

اطرح

6 sin (2 x - 3 0^{\circ}) + 2 - 2 = 0 - 2

بسّط

6 sin (2 x - 3 0^{\circ}) = - 2

6 sin (2 x - 3 0^{\circ}) = - 2

6

اقسم الطرفين على

6 sin (2 x - 3 0^{\circ}) = - 2

6

اقسم الطرفين على

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6} = \frac{- 2}{6}

بسّط

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6} = \frac{- 2}{6}

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6}

بسّط:

sin (2 x - 3 0^{\circ})

\frac{6 sin ( 2 x - 3 0 ^{\circ} )}{6}

\frac{6}{6} = 1 :

اقسم الأعداد

= sin (2 x - 3 0^{\circ})

\frac{- 2}{6}

بسّط:

- \frac{1}{3}

\frac{- 2}{6}

\frac{- a}{b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{2}{6}

2 :

إلغ العوامل المشتركة

= - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

Apply trig inverse properties

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

sin (2 x - 3 0^{\circ}) = - \frac{1}{3} :

حلول عامّة لـ

sin (x) = - a \Rightarrow x = arcsin (- a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n

arcsin (- \frac{1}{3}) + 36 0^{\circ} n

بسّط:

- arcsin (\frac{1}{3}) + 36 0^{\circ} n

arcsin (- \frac{1}{3}) + 36 0^{\circ} n

arcsin (- x) = - arcsin (x) :

استخدم القانون التالي

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 36 0^{\circ} n

2 x - 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n

انقل

3 0^{\circ}

إلى الجانب الأيمن

2 x - 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n

للطرفين

3 0^{\circ}

أضف

2 x - 3 0^{\circ} + 3 0^{\circ} = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

بسّط

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2

اقسم الطرفين على

2 x = - arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2

اقسم الطرفين على

\frac{2 x}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

بسّط

\frac{2 x}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

بسّط:

18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} - \frac{arcsin ( \frac{1}{3} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{6 \cdot 2}

6 \cdot 2 = 12 :

اضرب الأعداد

= 1 5^{\circ}

= 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

انقل

3 0^{\circ}

إلى الجانب الأيمن

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

للطرفين

3 0^{\circ}

أضف

2 x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

بسّط

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2

اقسم الطرفين على

2 x = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n + 3 0^{\circ}

2

اقسم الطرفين على

\frac{2 x}{2} = 9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

بسّط

\frac{2 x}{2} = 9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

بسّط:

18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

9 0^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

جمّع التعابير المتشابهة

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{6 \cdot 2}

6 \cdot 2 = 12 :

اضرب الأعداد

= 1 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

جمّع التعابير المتشابهة

= 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

أظهر الحلّ بالتمثيل العشريّ

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

رسم

أمثلة شائعة

sin(x)=sin(pi/(10))

sin (x) = sin (\frac{π}{10})

sin(3x)-sin(x)=-2sin(2x)sin(x)

sin (3 x) - sin (x) = - 2 sin (2 x) sin (x)

solvefor x,0.05cos(x)=-sin(x)

so l v e f or x, 0.05 cos (x) = - sin (x)

cos(θ)= 3/10

cos (θ) = \frac{3}{10}

tan(x)= 8/17

tan (x) = \frac{8}{17}