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شائع علم المثلثات >

cos(arctan(sqrt(3))+arcsin(1/3))

الحلّ

cos (arctan (3) + arcsin (\frac{1}{3}))

الحلّ

\frac{2}{3} - \frac{3}{6}

+1

عشري

0.18272 \dots

خطوات الحلّ

cos (arctan (3) + arcsin (\frac{1}{3}))

Rewrite using trig identities:

cos (arctan (3)) cos (arcsin (\frac{1}{3})) - sin (arctan (3)) sin (arcsin (\frac{1}{3}))

cos (arctan (3) + arcsin (\frac{1}{3}))

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

:فعّل متطابقة الجمع لزوايا

= cos (arctan (3)) cos (arcsin (\frac{1}{3})) - sin (arctan (3)) sin (arcsin (\frac{1}{3}))

= cos (arctan (3)) cos (arcsin (\frac{1}{3})) - sin (arctan (3)) sin (arcsin (\frac{1}{3}))

Rewrite using trig identities:

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

cos (arctan (3))

Rewrite using trig identities:

cos (arctan (3)) = \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

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

استخدم المتطابقة التالية

= \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

= \frac{1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

بسّط

= \frac{1}{2}

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

= 1 - (\frac{1}{3})^{2}

= 1 - (\frac{1}{3})^{2}

بسّط

= \frac{2 2}{3}

Rewrite using trig identities:

sin (arctan (3)) = \frac{3}{2}

sin (arctan (3))

Rewrite using trig identities:

sin (arctan (3)) = \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

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

استخدم المتطابقة التالية

= \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

= \frac{3 1 + ( 3 ) ^{2}}{1 + ( 3 ) ^{2}}

بسّط

= \frac{3}{2}

Rewrite using trig identities:

sin (arcsin (\frac{1}{3})) = \frac{1}{3}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{1}{3}

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

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

بسّط:

\frac{2}{3} - \frac{3}{6}

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

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

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

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

:اضرب كسور

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

2 :

إلغ العوامل المشتركة

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

1 \cdot 2 = 2 :

اضرب

= \frac{2}{3}

\frac{3}{2} \cdot \frac{1}{3} = \frac{3}{6}

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

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

:اضرب كسور

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

3 \cdot 1 = 3 :

اضرب

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

2 \cdot 3 = 6 :

اضرب الأعداد

= \frac{3}{6}

= \frac{2}{3} - \frac{3}{6}

= \frac{2}{3} - \frac{3}{6}

أمثلة شائعة

tan((5pi)/6-(5pi)/4)

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sin (\frac{π}{4} - \frac{π}{2})

sec (2 6^{\circ})