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العربية

1.16cos(θ)+0.532cos(θ)-0.557=0

الحلّ

1.16 cos (θ) + 0.532 cos (θ) - 0.557 = 0

θ = 1.23534 \dots + 2 πn, θ = 2 π - 1.23534 \dots + 2 πn

درجات

θ = 70.78000 \dots^{\circ} + 36 0^{\circ} n, θ = 289.21999 \dots^{\circ} + 36 0^{\circ} n

خطوات الحلّ

1.16 cos (θ) + 0.532 cos (θ) - 0.557 = 0

1.16 cos (θ) + 0.532 cos (θ) - 0.557

بسّط:

1.692 cos (θ) - 0.557

1.16 cos (θ) + 0.532 cos (θ) - 0.557

1.16 cos (θ) + 0.532 cos (θ) = 1.692 cos (θ) :

اجمع العناصر المتشابهة

= 1.692 cos (θ) - 0.557

1.692 cos (θ) - 0.557 = 0

1000

اضرب الطرفين بـ

1.692 cos (θ) - 0.557 = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1.692 cos (θ) \cdot 1000 - 0.557 \cdot 1000 = 0 \cdot 1000

بسّط

1692 cos (θ) - 557 = 0

1692 cos (θ) - 557 = 0

انقل

557

إلى الجانب الأيمن

1692 cos (θ) - 557 = 0

للطرفين

557

أضف

1692 cos (θ) - 557 + 557 = 0 + 557

بسّط

1692 cos (θ) = 557

1692 cos (θ) = 557

1692

اقسم الطرفين على

1692 cos (θ) = 557

1692

اقسم الطرفين على

\frac{1692 cos ( θ )}{1692} = \frac{557}{1692}

بسّط

cos (θ) = \frac{557}{1692}

cos (θ) = \frac{557}{1692}

Apply trig inverse properties

cos (θ) = \frac{557}{1692}

cos (θ) = \frac{557}{1692} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{557}{1692}) + 2 πn, θ = 2 π - arccos (\frac{557}{1692}) + 2 πn

θ = arccos (\frac{557}{1692}) + 2 πn, θ = 2 π - arccos (\frac{557}{1692}) + 2 πn

أظهر الحلّ بالتمثيل العشريّ

θ = 1.23534 \dots + 2 πn, θ = 2 π - 1.23534 \dots + 2 πn

arcsin (6 x) + arcsin (63 x) = - \frac{π}{2}

cos (x) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

4 + 4 sin (θ) = \frac{3}{1 - sin ( θ )}

so l v e f or x, z = arctan (x y)

(sin (x) - 5) (sin (x) - 1) = 0