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sin(pi/6)+cos(2 pi/6)

الحلّ

sin (\frac{π}{6}) + cos (2 \frac{π}{6})

الحلّ

1

خطوات الحلّ

sin (\frac{π}{6}) + cos (2 \cdot \frac{π}{6})

استخدم المتطابقة الأساسيّة التالية:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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}

Rewrite using trig identities:

cos (2 \cdot \frac{π}{6}) = \frac{1}{2}

cos (2 \cdot \frac{π}{6})

بسّط:

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

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

:اضرب كسور

= \frac{π 2}{6}

2 :

إلغ العوامل المشتركة

= \frac{π}{3}

= cos (\frac{π}{3})

استخدم المتطابقة الأساسيّة التالية:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{1}{2}

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

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

بسّط:

1

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

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

فعّل القانون

= \frac{1 + 1}{2}

1 + 1 = 2 :

اجمع الأعداد

= \frac{2}{2}

\frac{a}{a} = 1

فعّل القانون

= 1

= 1

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