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شائع علم المثلثات >

50sin(45)=600sin(θ)

الحلّ

50 sin (4 5^{\circ}) = 600 sin (θ)

الحلّ

θ = 0.05895 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.05895 \dots + 36 0^{\circ} n

+1

راديان

θ = 0.05895 \dots + 2 πn, θ = π - 0.05895 \dots + 2 πn

خطوات الحلّ

50 sin (4 5^{\circ}) = 600 sin (θ)

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{2}{2}

50 \cdot \frac{2}{2} = 600 sin (θ)

بدّل الأطراف

600 sin (θ) = 50 \cdot \frac{2}{2}

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

:اضرب كسور

600 sin (θ) = \frac{2 \cdot 50}{2}

\frac{50}{2} = 25 :

اقسم الأعداد

600 sin (θ) = 252

600

اقسم الطرفين على

600 sin (θ) = 252

600

اقسم الطرفين على

\frac{600 sin ( θ )}{600} = \frac{25 2}{600}

بسّط

sin (θ) = \frac{2}{24}

sin (θ) = \frac{2}{24}

Apply trig inverse properties

sin (θ) = \frac{2}{24}

sin (θ) = \frac{2}{24} :

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 (\frac{2}{24}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{2}{24}) + 36 0^{\circ} n

θ = arcsin (\frac{2}{24}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{2}{24}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

θ = 0.05895 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.05895 \dots + 36 0^{\circ} n

رسم

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