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شائع علم المثلثات >

885cos(θ)-70=cos(250)+250

الحلّ

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

الحلّ

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

+1

راديان

θ = 1.48705 \dots + 2 πn, θ = 2 π - 1.48705 \dots + 2 πn

خطوات الحلّ

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

انقل

70

إلى الجانب الأيمن

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

للطرفين

70

أضف

885 cos (θ) - 70 + 70 = cos (25 0^{\circ}) + 25 0^{\circ} + 70

بسّط

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

885

اقسم الطرفين على

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

885

اقسم الطرفين على

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

بسّط

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

\frac{885 cos ( θ )}{885}

بسّط:

cos (θ)

\frac{885 cos ( θ )}{885}

\frac{885}{885} = 1 :

اقسم الأعداد

= cos (θ)

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

بسّط:

\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

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

فعّل القانون

= \frac{cos ( 25 0 ^{\circ} ) + 25 0 ^{\circ} + 70}{885}

cos (25 0^{\circ}) + 25 0^{\circ} + 70

وحّد:

\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

cos (25 0^{\circ}) + 25 0^{\circ} + 70

cos (25 0^{\circ}) = \frac{cos ( 25 0 ^{\circ} ) 18}{18}, 70 = \frac{70 \cdot 18}{18}

:حوّل الأعداد لكسور

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18}{18} + 25 0^{\circ} + \frac{70 \cdot 18}{18}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 70 \cdot 18}{18}

70 \cdot 18 = 1260 :

اضرب الأعداد

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

= \frac{\frac{18 c o s ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}}{885}

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

: استخدم ميزات الكسور التالية

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 1260}{18 \cdot 885}

18 \cdot 885 = 15930 :

اضرب الأعداد

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

Apply trig inverse properties

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930} :

حلول عامّة لـ

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

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

أظهر الحلّ بالتمثيل العشريّ

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

رسم

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