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شائع >

500=538.5cos(x-10)

الحلّ

500 = 538.5 cos (x - 1 0^{\circ})

الحلّ

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

راديان

x = 0.38042 \dots + \frac{π}{18} + 2 πn, x = 2 π - 0.38042 \dots + \frac{π}{18} + 2 πn

خطوات الحلّ

500 = 538.5 cos (x - 1 0^{\circ})

بدّل الأطراف

538.5 cos (x - 1 0^{\circ}) = 500

10

اضرب الطرفين بـ

538.5 cos (x - 1 0^{\circ}) = 500

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

538.5 cos (x - 1 0^{\circ}) \cdot 10 = 500 \cdot 10

بسّط

5385 cos (x - 1 0^{\circ}) = 5000

5385 cos (x - 1 0^{\circ}) = 5000

5385

اقسم الطرفين على

5385 cos (x - 1 0^{\circ}) = 5000

5385

اقسم الطرفين على

\frac{5385 cos ( x - 1 0 ^{\circ} )}{5385} = \frac{5000}{5385}

بسّط

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

Apply trig inverse properties

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

cos (x - 1 0^{\circ}) = \frac{1000}{1077} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n

حلّ:

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n

انقل

1 0^{\circ}

إلى الجانب الأيمن

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n

للطرفين

1 0^{\circ}

أضف

x - 1 0^{\circ} + 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

بسّط

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

حلّ:

x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

انقل

1 0^{\circ}

إلى الجانب الأيمن

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

للطرفين

1 0^{\circ}

أضف

x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

بسّط

x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

أظهر الحلّ بالتمثيل العشريّ

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

رسم

أمثلة شائعة

-2cos^2(x)=3(sin(x)-1)

- 2 cos^{2} (x) = 3 (sin (x) - 1)

cos(x)tan(x)=sin(2x)

cos (x) tan (x) = sin (2 x)

2|sin(4θ)|=0

2 ∣ sin (4 θ) ∣ = 0

250sin(75)=393.19sin(45-θ)

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

tan(θ)= 6/(6.71)

tan (θ) = \frac{6}{6.71}