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شائع علم المثلثات >

cos(arcsin(1/2)+arccos(4/5))

الحلّ

cos (arcsin (\frac{1}{2}) + arccos (\frac{4}{5}))

الحلّ

\frac{2 3}{5} - \frac{3}{10}

+1

عشري

0.39282 \dots

خطوات الحلّ

cos (arcsin (\frac{1}{2}) + arccos (\frac{4}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) cos (arccos (\frac{4}{5})) - sin (arcsin (\frac{1}{2})) sin (arccos (\frac{4}{5}))

cos (arcsin (\frac{1}{2}) + arccos (\frac{4}{5}))

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

:فعّل متطابقة الجمع لزوايا

= cos (arcsin (\frac{1}{2})) cos (arccos (\frac{4}{5})) - sin (arcsin (\frac{1}{2})) sin (arccos (\frac{4}{5}))

= cos (arcsin (\frac{1}{2})) cos (arccos (\frac{4}{5})) - sin (arcsin (\frac{1}{2})) sin (arccos (\frac{4}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = \frac{3}{2}

cos (arcsin (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

cos (arcsin (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

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

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

بسّط

= \frac{3}{2}

Rewrite using trig identities:

cos (arccos (\frac{4}{5})) = \frac{4}{5}

cos (arccos (x)) = x :

استخدم المتطابقة التالية

= \frac{4}{5}

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{1}{2}

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) = \frac{3}{5}

sin (arccos (\frac{4}{5}))

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) = 1 - (\frac{4}{5})^{2}

sin (arccos (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

= 1 - (\frac{4}{5})^{2}

= 1 - (\frac{4}{5})^{2}

بسّط

= \frac{3}{5}

= \frac{3}{2} \cdot \frac{4}{5} - \frac{1}{2} \cdot \frac{3}{5}

\frac{3}{2} \cdot \frac{4}{5} - \frac{1}{2} \cdot \frac{3}{5}

بسّط:

\frac{2 3}{5} - \frac{3}{10}

\frac{3}{2} \cdot \frac{4}{5} - \frac{1}{2} \cdot \frac{3}{5}

\frac{3}{2} \cdot \frac{4}{5} = \frac{2 3}{5}

\frac{3}{2} \cdot \frac{4}{5}

2

اختزل العامل المشترك قطريًا

= \frac{3}{1} \cdot \frac{2}{5}

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

:اضرب كسور

= \frac{3 \cdot 2}{1 \cdot 5}

1 \cdot 5 = 5 :

اضرب الأعداد

= \frac{2 3}{5}

\frac{1}{2} \cdot \frac{3}{5} = \frac{3}{10}

\frac{1}{2} \cdot \frac{3}{5}

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

:اضرب كسور

= \frac{1 \cdot 3}{2 \cdot 5}

1 \cdot 3 = 3 :

اضرب الأعداد

= \frac{3}{2 \cdot 5}

2 \cdot 5 = 10 :

اضرب الأعداد

= \frac{3}{10}

= \frac{2 3}{5} - \frac{3}{10}

= \frac{2 3}{5} - \frac{3}{10}

أمثلة شائعة

arccos (\frac{8}{13})

sin (\frac{13}{2} π)

cos (3.1416)

-13.5cos(pi/6*45)+14.5

- 13.5 cos (\frac{π}{6} \cdot 45) + 14.5

(250)/(cos(50))

\frac{250}{cos ( 5 0 ^{\circ} )}