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شائع علم المثلثات >

6cos(45)+2sin(45)+4tan(45)

الحلّ

6 cos (4 5^{\circ}) + 2 sin (4 5^{\circ}) + 4 tan (4 5^{\circ})

الحلّ

42 + 4

+1

عشري

9.65685 \dots

خطوات الحلّ

6 cos (4 5^{\circ}) + 2 sin (4 5^{\circ}) + 4 tan (4 5^{\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 (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

استخدم المتطابقة الأساسيّة التالية:

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

tan (4 5^{\circ})

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}

= 1

= 6 \cdot \frac{2}{2} + 2 \cdot \frac{2}{2} + 4 \cdot 1

6 \cdot \frac{2}{2} + 2 \cdot \frac{2}{2} + 4 \cdot 1

بسّط:

42 + 4

6 \cdot \frac{2}{2} + 2 \cdot \frac{2}{2} + 4 \cdot 1

6 \cdot \frac{2}{2} + 2 \cdot \frac{2}{2} = 8 \cdot \frac{2}{2} :

اجمع العناصر المتشابهة

= 8 \cdot \frac{2}{2} + 4 \cdot 1

8 \cdot \frac{2}{2} = 42

8 \cdot \frac{2}{2}

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

:اضرب كسور

= \frac{2 \cdot 8}{2}

\frac{8}{2} = 4 :

اقسم الأعداد

= 42

4 \cdot 1 = 4

4 \cdot 1

4 \cdot 1 = 4 :

اضرب الأعداد

= 4

= 42 + 4

= 42 + 4

أمثلة شائعة

sin^{2} (8 1^{\circ})

2 cos (\frac{3 π}{9})

cos (- 2 \cdot π)

tan(arccos(3/5)+arcsin(4/5))

tan (arccos (\frac{3}{5}) + arcsin (\frac{4}{5}))

tan (7 0^{\circ}) \cdot 10