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شائع علم المثلثات >

solvefor y,arctan(y)+1/2 (1-t)^2=c

الحلّ

solve for

y, arctan (y) + \frac{1}{2} (1 - t)^{2} = c

الحلّ

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

خطوات الحلّ

arctan (y) + \frac{1}{2} (1 - t)^{2} = c

انقل

\frac{1}{2} (1 - t)^{2}

إلى الجانب الأيمن

arctan (y) + \frac{1}{2} (1 - t)^{2} = c

من الطرفين

\frac{1}{2} (1 - t)^{2}

اطرح

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = c - \frac{1}{2} (1 - t)^{2}

بسّط

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = c - \frac{1}{2} (1 - t)^{2}

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2}

بسّط:

arctan (y)

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2}

\frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = 0 :

اجمع العناصر المتشابهة

= arctan (y)

c - \frac{1}{2} (1 - t)^{2}

بسّط:

c - \frac{1}{2} + t - \frac{1}{2} t^{2}

c - \frac{1}{2} (1 - t)^{2}

(1 - t)^{2} : 1 - 2 t + t^{2}

(a - b)^{2} = a^{2} - 2 ab + b^{2}

:فعّل صيغة الضرب المختصر

a = 1, b = t

= 1^{2} - 2 \cdot 1 \cdot t + t^{2}

1^{2} - 2 \cdot 1 \cdot t + t^{2}

بسّط:

1 - 2 t + t^{2}

1^{2} - 2 \cdot 1 \cdot t + t^{2}

1^{a} = 1

فعّل القانون

1^{2} = 1

= 1 - 2 \cdot 1 \cdot t + t^{2}

2 \cdot 1 = 2 :

اضرب الأعداد

= 1 - 2 t + t^{2}

= 1 - 2 t + t^{2}

= c - \frac{1}{2} (1 - 2 t + t^{2})

- \frac{1}{2} (1 - 2 t + t^{2})

وسٌع:

- \frac{1}{2} + t - \frac{1}{2} t^{2}

- \frac{1}{2} (1 - 2 t + t^{2})

فعّل قانون ضرب الأقواس

= (- \frac{1}{2}) \cdot 1 + (- \frac{1}{2}) (- 2 t) + (- \frac{1}{2}) t^{2}

فعّل قوانين سالب-موجب

+ (- a) = - a, (- a) (- b) = ab

= - 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2}

- 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2}

بسّط:

- \frac{1}{2} + t - \frac{1}{2} t^{2}

- 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2}

1 \cdot \frac{1}{2} = \frac{1}{2}

1 \cdot \frac{1}{2}

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

اضرب

= \frac{1}{2}

2 \cdot \frac{1}{2} t = t

2 \cdot \frac{1}{2} t

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

:اضرب كسور

= \frac{1 \cdot 2}{2} t

2 :

إلغ العوامل المشتركة

= t \cdot 1

t \cdot 1 = t :

اضرب

= t

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

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

= c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

Apply trig inverse properties

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (x) = a \Rightarrow x = tan (a)

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

رسم

أمثلة شائعة

(15-sqrt(3))/3 =5-2/3*csc(4x+pi/2)

\frac{15 - 3}{3} = 5 - \frac{2}{3} \cdot csc (4 x + \frac{π}{2})

tan(x)+4sin(x)=0

tan (x) + 4 sin (x) = 0

1 + 2 \cdot sin (x) = 2

1 + 2 \cdot sin (x) = 3

sin(α)=(120sin(60))/(1200)

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}