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شائع علم المثلثات >

189.4=100tan^2(45-x/2)

الحلّ

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

الحلّ

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

راديان

x = \frac{π}{2} - 2 \cdot 0.94242 \dots - 2 πn, x = \frac{π}{2} + 2 \cdot 0.94242 \dots - 2 πn

خطوات الحلّ

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

بدّل الأطراف

100 tan^{2} (4 5^{\circ} - \frac{x}{2}) = 189.4

بالاستعانة بطريقة التعويض

100 tan^{2} (4 5^{\circ} - \frac{x}{2}) = 189.4

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

على افتراض أنّ

100 u^{2} = 189.4

100 u^{2} = 189.4 : u = 1.894, u = - 1.894

100 u^{2} = 189.4

100

اقسم الطرفين على

100 u^{2} = 189.4

100

اقسم الطرفين على

\frac{100 u ^{2}}{100} = \frac{189.4}{100}

بسّط

u^{2} = 1.894

u^{2} = 1.894

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

الحلول هي

x^{2} = f (a)

لـ

u = 1.894, u = - 1.894

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

استبدل مجددًا

tan (4 5^{\circ} - \frac{x}{2}) = 1.894, tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894, tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = 1.894

Apply trig inverse properties

tan (4 5^{\circ} - \frac{x}{2}) = 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894 :

حلول عامّة لـ

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

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

حلّ:

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} - \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} - \frac{x}{2} - 4 5^{\circ} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

- \frac{x}{2} = arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

2 (- \frac{x}{2}) = 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط

2 (- \frac{x}{2}) = 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 (- \frac{x}{2})

بسّط:

- x

2 (- \frac{x}{2})

(- a) = - a

:احذف الأقواس

= - 2 \cdot \frac{x}{2}

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

:اضرب كسور

= - \frac{x \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= - x

2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط:

2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (1.894) + 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 (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 1

اقسم الطرفين على

- x = 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

\frac{- x}{- 1}

بسّط:

x

\frac{- x}{- 1}

\frac{- a}{- b} = \frac{a}{b}

: استخدم ميزات الكسور التالية

= \frac{x}{1}

\frac{a}{1} = a

فعّل القانون

= x

\frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

بسّط:

- 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( 1.894 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{36 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( 1.894 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{9 0 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{2 arctan ( 1.894 )}{- 1} = - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{2 arctan ( 1.894 )}{1}

\frac{a}{1} = a

فعّل القانون

= - 2 arctan (1.894)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - 2 arctan (1.894)

- (- a) = a

فعّل القانون

= - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

Apply trig inverse properties

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894 :

حلول عامّة لـ

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

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

حلّ:

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

4 5^{\circ} - \frac{x}{2} = arctan (- 1.894) + 18 0^{\circ} n

arctan (- 1.894) + 18 0^{\circ} n

بسّط:

- arctan (1.894) + 18 0^{\circ} n

arctan (- 1.894) + 18 0^{\circ} n

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

استخدم القانون التالي

arctan (- 1.894) = - arctan (1.894)

= - arctan (1.894) + 18 0^{\circ} n

4 5^{\circ} - \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} - \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} - \frac{x}{2} - 4 5^{\circ} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

- \frac{x}{2} = - arctan (1.894) + 18 0^{\circ} n - 4 5^{\circ}

2

اضرب الطرفين بـ

2 (- \frac{x}{2}) = - 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط

2 (- \frac{x}{2}) = - 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 (- \frac{x}{2})

بسّط:

- x

2 (- \frac{x}{2})

(- a) = - a

:احذف الأقواس

= - 2 \cdot \frac{x}{2}

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

:اضرب كسور

= - \frac{x \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= - x

- 2 arctan (1.894) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

بسّط:

- 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (1.894) + 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 (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 1

اقسم الطرفين على

- x = - 2 arctan (1.894) + 36 0^{\circ} n - 9 0^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = - \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = - \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

\frac{- x}{- 1}

بسّط:

x

\frac{- x}{- 1}

\frac{- a}{- b} = \frac{a}{b}

: استخدم ميزات الكسور التالية

= \frac{x}{1}

\frac{a}{1} = a

فعّل القانون

= x

- \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

بسّط:

- 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

- \frac{2 arctan ( 1.894 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{2 arctan ( 1.894 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{36 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} - \frac{2 arctan ( 1.894 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{9 0 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{2 arctan ( 1.894 )}{- 1} = - 2 arctan (1.894)

\frac{2 arctan ( 1.894 )}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{2 arctan ( 1.894 )}{1}

\frac{a}{1} = a

فعّل القانون

= - 2 arctan (1.894)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - (- 2 arctan (1.894))

- (- a) = a

فعّل القانون

= - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

وحّد الحلول

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894), x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

أظهر الحلّ بالتمثيل العشريّ

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

رسم

أمثلة شائعة

20/3 sin(10x)+5cos(10x)=0

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

cos(3x+pi/4)=-(sqrt(3))/2

cos (3 x + \frac{π}{4}) = - \frac{3}{2}

sin(x)-1/4 =0

sin (x) - \frac{1}{4} = 0

sqrt(2)csc(θ)-2=0

2 csc (θ) - 2 = 0

sin(θ)=(sqrt(5))/4

sin (θ) = \frac{5}{4}