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شائع >

1715/70 =tan(45+θ/2)

الحلّ

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

الحلّ

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

راديان

θ = 2 \cdot 1.53000 \dots - \frac{π}{2} + 2 πn

خطوات الحلّ

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

بدّل الأطراف

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

35 :

إلغ العوامل المشتركة

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Apply trig inverse properties

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2} :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

حلّ:

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} + \frac{θ}{2} - 4 5^{\circ} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

\frac{2 θ}{2}

بسّط:

θ

\frac{2 θ}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= θ

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط:

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

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

:اضرب كسور

= 9 0^{\circ}

2 :

إلغ العوامل المشتركة

= 9 0^{\circ}

= 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

أظهر الحلّ بالتمثيل العشريّ

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

رسم

أمثلة شائعة

sin(θ)=-(sqrt(3))/2 ,pi<θ<(3pi)/2

sin (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}

cos(3x)=sin(x-30)

cos (3 x) = sin (x - 3 0^{\circ})

4sin(θ)=4cos(2θ)

4 sin (θ) = 4 cos (2 θ)

tan (5 θ + 30) = 1

885cos(θ)-70=cos(250)

885 cos (θ) - 70 = cos (25 0^{\circ})