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شائع علم المثلثات >

0.56=tan^2(45+x/2)

الحلّ

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

الحلّ

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

راديان

x = 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn, x = - 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn

خطوات الحلّ

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

بدّل الأطراف

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

بالاستعانة بطريقة التعويض

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

tan (4 5^{\circ} + \frac{x}{2}) = u :

على افتراض أنّ

u^{2} = 0.56

u^{2} = 0.56 : u = 0.56, u = - 0.56

u^{2} = 0.56

x = f (a), - f (a)

الحلول هي

x^{2} = f (a)

لـ

u = 0.56, u = - 0.56

u = tan (4 5^{\circ} + \frac{x}{2})

استبدل مجددًا

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56 : x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

Apply trig inverse properties

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56 :

حلول عامّة لـ

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

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

حلّ:

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط:

2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (0.56) + 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 (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56 : x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

Apply trig inverse properties

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56 :

حلول عامّة لـ

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

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

حلّ:

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

arctan (- 0.56) + 18 0^{\circ} n

بسّط:

- arctan (\frac{14}{5}) + 18 0^{\circ} n

arctan (- 0.56) + 18 0^{\circ} n

arctan (- 0.56) = - arctan (\frac{14}{5})

arctan (- 0.56)

= arctan (- \frac{14}{25})

arctan (- x) = - arctan (x) :

استخدم القانون التالي

arctan (- \frac{14}{25}) = - arctan (\frac{14}{25})

= - arctan (\frac{14}{25})

= - arctan (\frac{14}{5})

= - arctan (\frac{14}{5}) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط:

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (\frac{14}{5}) + 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{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

وحّد الحلول

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

أظهر الحلّ بالتمثيل العشريّ

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

رسم

أمثلة شائعة

5sec^2(x)-14tan(x)=8

5 sec^{2} (x) - 14 tan (x) = 8

25 cos^{2} (x) = 16

solvefor y,arcsin(y)=ln(x)

so l v e f or y, arcsin (y) = ln (x)

sin(9x+6)=cos(3x-4)

sin (9 x + 6) = cos (3 x - 4)

csc(x)= 1/(sec(x))

csc (x) = \frac{1}{sec ( x )}