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شائع علم المثلثات >

-0.002=sin(2pi*(3)-500pi(0)+x)

الحلّ

- 0.002 = sin (2 π \cdot (3) - 500 π (0) + x)

الحلّ

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

+1

درجات

x = - 1080.11459 \dots^{\circ} + 36 0^{\circ} n, x = - 899.88540 \dots^{\circ} + 36 0^{\circ} n

خطوات الحلّ

- 0.002 = sin (2 π (3) - 500 π (0) + x)

بدّل الأطراف

sin (2 π 3 - 500 π 0 + x) = - 0.002

Apply trig inverse properties

sin (2 π 3 - 500 π 0 + x) = - 0.002

sin (2 π 3 - 500 π 0 + x) = - 0.002 :

حلول عامّة لـ

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn

حلّ:

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn

2 π 3 - 500 π 0 + x

بسّط:

x + 6 π

2 π 3 - 500 π 0 + x

2 \cdot 3 = 6 :

اضرب الأعداد

= 6 π - 500 \cdot 0 π + x

0 \cdot a = 0

فعّل القانون

= 6 π - 0 + x

6 π - 0 + x = 6 π + x

= x + 6 π

arcsin (- 0.002) + 2 πn

بسّط:

- arcsin (\frac{1}{500}) + 2 πn

arcsin (- 0.002) + 2 πn

arcsin (- 0.002) = - arcsin (\frac{1}{500})

arcsin (- 0.002)

= arcsin (- \frac{1}{500})

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

استخدم القانون التالي

arcsin (- \frac{1}{500}) = - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500}) + 2 πn

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

انقل

6 π

إلى الجانب الأيمن

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

من الطرفين

6 π

اطرح

x + 6 π - 6 π = - arcsin (\frac{1}{500}) + 2 πn - 6 π

بسّط

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

حلّ:

x = - 5 π + 2 πn + arcsin (0.002)

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

2 \cdot 3 = 6 :

اضرب الأعداد

6 π - 500 \cdot 0 π + x = π + arcsin (0.002) + 2 πn

0 \cdot a = 0

فعّل القانون

6 π - 0 + x = π + arcsin (0.002) + 2 πn

6 π - 0 + x = 6 π + x

x + 6 π = π + arcsin (0.002) + 2 πn

انقل

6 π

إلى الجانب الأيمن

x + 6 π = π + arcsin (0.002) + 2 πn

من الطرفين

6 π

اطرح

x + 6 π - 6 π = π + arcsin (0.002) + 2 πn - 6 π

بسّط

x = - 5 π + 2 πn + arcsin (0.002)

x = - 5 π + 2 πn + arcsin (0.002)

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π, x = - 5 π + 2 πn + arcsin (0.002)

أظهر الحلّ بالتمثيل العشريّ

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

رسم

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