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شائع علم المثلثات >

5-tan^2(x)=4,0<= x<= 360

الحلّ

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

الحلّ

x = 4 5^{\circ}, x = 22 5^{\circ}, x = 13 5^{\circ}, x = 31 5^{\circ}

+1

راديان

x = \frac{π}{4}, x = \frac{5 π}{4}, x = \frac{3 π}{4}, x = \frac{7 π}{4}

خطوات الحلّ

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

بالاستعانة بطريقة التعويض

5 - tan^{2} (x) = 4

tan (x) = u :

على افتراض أنّ

5 - u^{2} = 4

5 - u^{2} = 4 : u = 1, u = - 1

5 - u^{2} = 4

انقل

5

إلى الجانب الأيمن

5 - u^{2} = 4

من الطرفين

5

اطرح

5 - u^{2} - 5 = 4 - 5

بسّط

- u^{2} = - 1

- u^{2} = - 1

- 1

اقسم الطرفين على

- u^{2} = - 1

- 1

اقسم الطرفين على

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

بسّط

u^{2} = 1

u^{2} = 1

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

الحلول هي

x^{2} = f (a)

لـ

u = 1, u = - 1

1 = 1

1

1 = 1

فعّل القانون

= 1

- 1 = - 1

- 1

1 = 1

فعّل القانون

= - 1

u = 1, u = - 1

u = tan (x)

استبدل مجددًا

tan (x) = 1, tan (x) = - 1

tan (x) = 1, tan (x) = - 1

tan (x) = 1, 0 \leq x \leq 36 0^{\circ} : x = 4 5^{\circ}, x = 22 5^{\circ}

tan (x) = 1, 0 \leq x \leq 36 0^{\circ}

tan (x) = 1 :

حلول عامّة لـ

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 4 5^{\circ} + 18 0^{\circ} n

x = 4 5^{\circ} + 18 0^{\circ} n

0 \leq x \leq 36 0^{\circ} :

حلول للمدى

x = 4 5^{\circ}, x = 22 5^{\circ}

tan (x) = - 1, 0 \leq x \leq 36 0^{\circ} : x = 13 5^{\circ}, x = 31 5^{\circ}

tan (x) = - 1, 0 \leq x \leq 36 0^{\circ}

tan (x) = - 1 :

حلول عامّة لـ

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 13 5^{\circ} + 18 0^{\circ} n

x = 13 5^{\circ} + 18 0^{\circ} n

0 \leq x \leq 36 0^{\circ} :

حلول للمدى

x = 13 5^{\circ}, x = 31 5^{\circ}

وحّد الحلول

x = 4 5^{\circ}, x = 22 5^{\circ}, x = 13 5^{\circ}, x = 31 5^{\circ}

رسم

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