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شائع علم المثلثات >

cos(150)+sin(45)+1/2 cot(-330)

الحلّ

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

الحلّ

\frac{2}{2}

+1

عشري

0.70710 \dots

خطوات الحلّ

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\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{3}{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}

Rewrite using trig identities:

cot (- 33 0^{\circ}) = 3

cot (- 33 0^{\circ})

cot (- x) = - cot (x) :

استخدم القانون التالي

cot (- 33 0^{\circ}) = - cot (33 0^{\circ})

= - cot (33 0^{\circ})

cot (33 0^{\circ}) = cot (15 0^{\circ})

cot (33 0^{\circ})

18 0^{\circ} + 15 0^{\circ}

كـ

33 0^{\circ}

اكتب مجددًا

= cot (18 0^{\circ} + 15 0^{\circ})

cot (x + 18 0^{\circ}) = cot (x)

:

cot :

استخدم دوريّة الـ

cot (18 0^{\circ} + 15 0^{\circ}) = cot (15 0^{\circ})

= cot (15 0^{\circ})

= - cot (15 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

cot (15 0^{\circ}) = - 3

cot (15 0^{\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

= - 3

= - (- 3)

بسّط

= 3

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

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

بسّط:

\frac{2}{2}

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

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

وحّد الكسور:

\frac{- 3 + 2}{2}

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

فعّل القانون

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

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

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

\frac{1}{2} 3

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

:اضرب كسور

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

1 \cdot 3 = 3 :

اضرب

= \frac{3}{2}

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

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

فعّل القانون

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

- 3 + 3 = 0 :

اجمع العناصر المتشابهة

= \frac{2}{2}

= \frac{2}{2}

أمثلة شائعة

arctan((8sqrt(3))/(-8))

arctan (\frac{8 3}{- 8})

- e^{0} cos (0)

cos (6 \cdot π)

cos(155)cos(20)+sin(155)sin(20)

cos (15 5^{\circ}) cos (2 0^{\circ}) + sin (15 5^{\circ}) sin (2 0^{\circ})

sin (3) (\frac{π}{2})