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شائع علم المثلثات >

(sin(x))/(45)=(sin(35))/(30)

الحلّ

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

الحلّ

x = 1.03598 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03598 \dots + 36 0^{\circ} n

+1

راديان

x = 1.03598 \dots + 2 πn, x = π - 1.03598 \dots + 2 πn

خطوات الحلّ

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

10

اضرب الطرفين بـ

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

10

اضرب الطرفين بـ

\frac{sin ( x )}{45} \cdot 10 = \frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

بسّط

\frac{sin ( x )}{45} \cdot 10 = \frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

\frac{sin ( x )}{45} \cdot 10

بسّط:

\frac{2 sin ( x )}{9}

\frac{sin ( x )}{45} \cdot 10

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

:اضرب كسور

= \frac{sin ( x ) \cdot 10}{45}

5 :

إلغ العوامل المشتركة

= \frac{2 sin ( x )}{9}

\frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

بسّط:

\frac{sin ( 3 5 ^{\circ} )}{3}

\frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

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

:اضرب كسور

= \frac{sin ( 3 5 ^{\circ} ) \cdot 10}{30}

10 :

إلغ العوامل المشتركة

= \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

9

اضرب الطرفين بـ

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

9

اضرب الطرفين بـ

\frac{9 \cdot 2 sin ( x )}{9} = \frac{9 sin ( 3 5 ^{\circ} )}{3}

بسّط

2 sin (x) = 3 sin (3 5^{\circ})

2 sin (x) = 3 sin (3 5^{\circ})

2

اقسم الطرفين على

2 sin (x) = 3 sin (3 5^{\circ})

2

اقسم الطرفين على

\frac{2 sin ( x )}{2} = \frac{3 sin ( 3 5 ^{\circ} )}{2}

بسّط

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

Apply trig inverse properties

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2} :

حلول عامّة لـ

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

x = arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n

x = arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

x = 1.03598 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03598 \dots + 36 0^{\circ} n

رسم

أمثلة شائعة

cos(x)=(4(-1/2)-1)/3

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

sec (y) = - 2

solvefor θ,y=-2+cos(3θ)

so l v e f or θ, y = - 2 + cos (3 θ)

cos(2x)+5*cos(x)=-3

cos (2 x) + 5 \cdot cos (x) = - 3

cos(x-(3pi)/2)= 1/2

cos (x - \frac{3 π}{2}) = \frac{1}{2}