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شائع علم المثلثات >

(sin(120))/(2.34)=(sin(θ))/(1.2)

الحلّ

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

الحلّ

θ = 0.46018 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46018 \dots + 36 0^{\circ} n

+1

راديان

θ = 0.46018 \dots + 2 πn, θ = π - 0.46018 \dots + 2 πn

خطوات الحلّ

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{3}{2}

\frac{\frac{3}{2}}{2.34} = \frac{sin ( θ )}{1.2}

بدّل الأطراف

\frac{sin ( θ )}{1.2} = \frac{\frac{3}{2}}{2.34}

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

: استخدم ميزات الكسور التالية

\frac{sin ( θ )}{1.2} = \frac{3}{2 \cdot 2.34}

2 \cdot 2.34 = 4.68 :

اضرب الأعداد

\frac{sin ( θ )}{1.2} = \frac{3}{4.68}

1.2

اضرب الطرفين بـ

\frac{sin ( θ )}{1.2} = \frac{3}{4.68}

1.2

اضرب الطرفين بـ

\frac{1.2 sin ( θ )}{1.2} = \frac{1.2 3}{4.68}

بسّط

\frac{1.2 sin ( θ )}{1.2} = \frac{1.2 3}{4.68}

\frac{1.2 sin ( θ )}{1.2}

بسّط:

sin (θ)

\frac{1.2 sin ( θ )}{1.2}

1.2 :

إلغ العوامل المشتركة

= sin (θ)

\frac{1.2 3}{4.68}

بسّط:

0.44411 \dots

\frac{1.2 3}{4.68}

حوّل لتمثيل عشريّ

3 = 1.73205 \dots

= \frac{1.2 \cdot 1.73205 \dots}{4.68}

1.2 \cdot 1.73205 \dots = 2.07846 \dots :

اضرب الأعداد

= \frac{2.07846 \dots}{4.68}

\frac{2.07846 \dots}{4.68} = 0.44411 \dots :

اقسم الأعداد

= 0.44411 \dots

sin (θ) = 0.44411 \dots

sin (θ) = 0.44411 \dots

sin (θ) = 0.44411 \dots

Apply trig inverse properties

sin (θ) = 0.44411 \dots

sin (θ) = 0.44411 \dots :

حلول عامّة لـ

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

θ = arcsin (0.44411 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.44411 \dots) + 36 0^{\circ} n

θ = arcsin (0.44411 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.44411 \dots) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

θ = 0.46018 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46018 \dots + 36 0^{\circ} n

رسم

أمثلة شائعة

tan (x) = \frac{12}{50}

sin(x)-2sin(x)*cos(x)=0

sin (x) - 2 sin (x) \cdot cos (x) = 0

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

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

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

sin (x) = 0.88