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sin^2(pi/6)+cos^2(pi/3)

الحلّ

sin^{2} (\frac{π}{6}) + cos^{2} (\frac{π}{3})

الحلّ

\frac{1}{2}

+1

العشري

0.5

خطوات الحلّ

sin^{2} (\frac{π}{6}) + cos^{2} (\frac{π}{3})

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}

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})^{2} + (\frac{1}{2})^{2}

(\frac{1}{2})^{2} + (\frac{1}{2})^{2}

بسّط:

\frac{1}{2}

(\frac{1}{2})^{2} + (\frac{1}{2})^{2}

(\frac{1}{2})^{2} + (\frac{1}{2})^{2} = 2 (\frac{1}{2})^{2} :

اجمع العناصر المتشابهة

= 2 (\frac{1}{2})^{2}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:فعّل قانون القوى

= \frac{1 ^{2}}{2 ^{2}}

1^{a} = 1

فعّل القانون

1^{2} = 1

= \frac{1}{2 ^{2}}

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

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

:اضرب كسور

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

1 \cdot 2 = 2 :

اضرب الأعداد

= \frac{2}{2 ^{2}}

2 :

إلغ العوامل المشتركة

= \frac{1}{2}

= \frac{1}{2}

أمثلة شائعة

sec(arcsin(-2))

sec (arcsin (- 2))

-cot((3pi)/4)*csc((3pi)/4)

- cot (\frac{3 π}{4}) \cdot csc (\frac{3 π}{4})

arctan (\frac{1}{42})

3.2 tan (2 3^{\circ})

arctan (\frac{- 7}{2})