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sec(60)-sin(30)+cot(45)

الحلّ

sec (6 0^{\circ}) - sin (3 0^{\circ}) + cot (4 5^{\circ})

الحلّ

\frac{5}{2}

+1

العشري

2.5

خطوات الحلّ

sec (6 0^{\circ}) - sin (3 0^{\circ}) + cot (4 5^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 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}

استخدم المتطابقة الأساسيّة التالية:

cot (4 5^{\circ}) = 1

cot (4 5^{\circ})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

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

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

بسّط:

\frac{5}{2}

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

2 + 1 = 3 :

اجمع الأعداد

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

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

:حوّل الأعداد لكسور

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

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

:بما أنّ المقامات متساوية، اجمع البسوط

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

3 \cdot 2 - 1 = 5

3 \cdot 2 - 1

3 \cdot 2 = 6 :

اضرب الأعداد

= 6 - 1

6 - 1 = 5 :

اطرح الأعداد

= 5

= \frac{5}{2}

= \frac{5}{2}

أمثلة شائعة

arcsec((1.46)/(1.47))

arcsec (\frac{1.46}{1.47})

8e^{8(1-1)}sec^2(e^{8(1-1)})-8e^{8(1-1)}

8 e^{8 (1 - 1)} sec^{2} (e^{8 (1 - 1)}) - 8 e^{8 (1 - 1)}

tan (\frac{4}{6})

arcsin(-1/(sqrt(5)))

arcsin (- \frac{1}{5})

sec (5 4^{\circ})