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شائع >

tan^2(45+x/3)=0.58

الحلّ

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

الحلّ

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

+1

راديان

x = 3 \cdot 0.65086 \dots - \frac{3 π}{4} + 3 πn, x = - 3 \cdot 0.65086 \dots - \frac{3 π}{4} + 3 πn

خطوات الحلّ

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

بالاستعانة بطريقة التعويض

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

tan (4 5^{\circ} + \frac{x}{3}) = u :

على افتراض أنّ

u^{2} = 0.58

u^{2} = 0.58 : u = 0.58, u = - 0.58

u^{2} = 0.58

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

الحلول هي

x^{2} = f (a)

لـ

u = 0.58, u = - 0.58

u = tan (4 5^{\circ} + \frac{x}{3})

استبدل مجددًا

tan (4 5^{\circ} + \frac{x}{3}) = 0.58, tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58, tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58 : x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

Apply trig inverse properties

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58 :

حلول عامّة لـ

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

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

حلّ:

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} + \frac{x}{3} = arctan (0.58) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

3

اضرب الطرفين بـ

\frac{x}{3} = arctan (0.58) + 18 0^{\circ} n - 4 5^{\circ}

3

اضرب الطرفين بـ

\frac{3 x}{3} = 3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

بسّط

\frac{3 x}{3} = 3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

\frac{3 x}{3}

بسّط:

x

\frac{3 x}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= x

3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

بسّط:

3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

3 arctan (0.58) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

3 \cdot 4 5^{\circ}

اضرب بـ:

13 5^{\circ}

3 \cdot 4 5^{\circ}

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

:اضرب كسور

= 13 5^{\circ}

= 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58 : x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

Apply trig inverse properties

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58 :

حلول عامّة لـ

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

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

حلّ:

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

4 5^{\circ} + \frac{x}{3} = arctan (- 0.58) + 18 0^{\circ} n

arctan (- 0.58) + 18 0^{\circ} n

بسّط:

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n

arctan (- 0.58) + 18 0^{\circ} n

arctan (- 0.58) = - arctan (\frac{58}{10})

arctan (- 0.58)

= arctan (- \frac{29}{50})

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

استخدم القانون التالي

arctan (- \frac{29}{50}) = - arctan (\frac{29}{50})

= - arctan (\frac{29}{50})

= - arctan (\frac{58}{10})

= - arctan (\frac{58}{10}) + 18 0^{\circ} n

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

حلل إلى عوامل:

229

58 = 2 \cdot 29

حلّل إلى عوامل

= 2 \cdot 29

n ab = n a n b

:فعْل قانون الجذور

= 229

10

حلل إلى عوامل:

2 \cdot 5

10 = 2 \cdot 5

حلّل إلى عوامل

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

اختزل:

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

انقل

4 5^{\circ}

إلى الجانب الأيمن

4 5^{\circ} + \frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n

من الطرفين

4 5^{\circ}

اطرح

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

بسّط

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ}

بسّط:

\frac{x}{3}

4 5^{\circ} + \frac{x}{3} - 4 5^{\circ}

4 5^{\circ} - 4 5^{\circ} = 0 :

اجمع العناصر المتشابهة

= \frac{x}{3}

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

بسّط:

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

- arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

= - arctan (\frac{58}{10}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

حلل إلى عوامل:

229

58 = 2 \cdot 29

حلّل إلى عوامل

= 2 \cdot 29

n ab = n a n b

:فعْل قانون الجذور

= 229

10

حلل إلى عوامل:

2 \cdot 5

10 = 2 \cdot 5

حلّل إلى عوامل

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

اختزل:

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

Could not simplify further

= - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

3

اضرب الطرفين بـ

\frac{x}{3} = - arctan (\frac{29}{5 2}) + 18 0^{\circ} n - 4 5^{\circ}

3

اضرب الطرفين بـ

\frac{3 x}{3} = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

بسّط

\frac{3 x}{3} = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

\frac{3 x}{3}

بسّط:

x

\frac{3 x}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= x

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

بسّط:

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

- 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

arctan (\frac{29}{5 2})

بسّط:

arctan (\frac{58}{10})

arctan (\frac{29}{5 2})

= arctan (\frac{58}{10})

= - 3 arctan (\frac{58}{10}) + 54 0^{\circ} n - 3 \cdot 4 5^{\circ}

3 \cdot 4 5^{\circ}

اضرب بـ:

13 5^{\circ}

3 \cdot 4 5^{\circ}

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

:اضرب كسور

= 13 5^{\circ}

= - 3 arctan (\frac{58}{10}) + 54 0^{\circ} n - 13 5^{\circ}

\frac{58}{10} = \frac{29}{5 2}

\frac{58}{10}

58

حلل إلى عوامل:

229

58 = 2 \cdot 29

حلّل إلى عوامل

= 2 \cdot 29

n ab = n a n b

:فعْل قانون الجذور

= 229

10

حلل إلى عوامل:

2 \cdot 5

10 = 2 \cdot 5

حلّل إلى عوامل

= \frac{2 29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

اختزل:

\frac{29}{2 \cdot 5}

\frac{2 29}{2 \cdot 5}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 29}{2 \cdot 5}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{29}{5 \cdot 2 ^{- \frac{1}{2} + 1}}

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{29}{5 \cdot 2 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

2^{\frac{1}{2}} = 2

= \frac{29}{5 2}

= \frac{29}{2 \cdot 5}

= - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

وحّد الحلول

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

أظهر الحلّ بالتمثيل العشريّ

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

رسم

أمثلة شائعة

1=4cos^2(x)-4cos(x)+2

1 = 4 cos^{2} (x) - 4 cos (x) + 2

1 = cos (3 θ)

3sin(2x)+cos(x)=0

3 sin (2 x) + cos (x) = 0

sinh (a x) = 0

8sin^4(x)-3sin^2(x)+1/4 =0

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0