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cos(15)= a/(55)

الحلّ

cos (1 5^{\circ}) = \frac{a}{55}

الحلّ

a = \frac{55 ( 6 + 2 )}{4}

+1

العشري

a = 53.12592 \dots

خطوات الحلّ

cos (1 5^{\circ}) = \frac{a}{55}

بدّل الأطراف

\frac{a}{55} = cos (1 5^{\circ})

cos (1 5^{\circ})

بسّط:

\frac{6 + 2}{4}

cos (1 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

cos (1 5^{\circ})

cos (4 5^{\circ} - 3 0^{\circ})

كـ

cos (1 5^{\circ})

أكتب

= cos (4 5^{\circ} - 3 0^{\circ})

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

:فعّل متطابقة الطرح لزوايا

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

استخدم المتطابقة الأساسيّة التالية:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

بسّط:

\frac{6 + 2}{4}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

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

:اضرب كسور

= \frac{2 3}{2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2 3}{4}

23

بسّط:

6

23

a b = a \cdot b

:فعْل قانون الجذور

23 = 2 \cdot 3

= 2 \cdot 3

2 \cdot 3 = 6 :

اضرب الأعداد

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

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

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

:اضرب كسور

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

2 \cdot 1 = 2 :

اضرب

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

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

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

فعّل القانون

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

\frac{a}{55} = \frac{6 + 2}{4}

55

اضرب الطرفين بـ

\frac{a}{55} = \frac{6 + 2}{4}

55

اضرب الطرفين بـ

\frac{55 a}{55} = \frac{55 ( 6 + 2 )}{4}

بسّط

a = \frac{55 ( 6 + 2 )}{4}

a = \frac{55 ( 6 + 2 )}{4}

أمثلة شائعة

tan^0(2x+15)=-1

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