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العربية

sin(arccos(2/3)-arctan(1/2))

الحلّ

sin (arccos (\frac{2}{3}) - arctan (\frac{1}{2}))

\frac{2}{3} - \frac{2 5}{15}

عشري

0.36852 \dots

خطوات الحلّ

sin (arccos (\frac{2}{3}) - arctan (\frac{1}{2}))

Rewrite using trig identities:

sin (arccos (\frac{2}{3})) cos (arctan (\frac{1}{2})) - cos (arccos (\frac{2}{3})) sin (arctan (\frac{1}{2}))

sin (arccos (\frac{2}{3}) - arctan (\frac{1}{2}))

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

:فعّل متطابقة الطرح لزوايا

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

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

Rewrite using trig identities:

sin (arccos (\frac{2}{3})) = \frac{5}{3}

sin (arccos (\frac{2}{3}))

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{5}{3}

Rewrite using trig identities:

cos (arctan (\frac{1}{2})) = \frac{2 5}{5}

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

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{2 5}{5}

Rewrite using trig identities:

cos (arccos (\frac{2}{3})) = \frac{2}{3}

cos (arccos (x)) = x :

استخدم المتطابقة التالية

= \frac{2}{3}

Rewrite using trig identities:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

sin (arctan (\frac{1}{2}))

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{5}{5}

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

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

بسّط:

\frac{2}{3} - \frac{2 5}{15}

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

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

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

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

:اضرب كسور

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

5 \cdot 25 = 10

5 \cdot 25

a a = a

:فعْل قانون الجذور

55 = 5

= 2 \cdot 5

2 \cdot 5 = 10 :

اضرب الأعداد

= 10

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

3 \cdot 5 = 15 :

اضرب الأعداد

= \frac{10}{15}

5 :

إلغ العوامل المشتركة

= \frac{2}{3}

\frac{2}{3} \cdot \frac{5}{5} = \frac{2 5}{15}

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

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

:اضرب كسور

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

3 \cdot 5 = 15 :

اضرب الأعداد

= \frac{2 5}{15}

= \frac{2}{3} - \frac{2 5}{15}

= \frac{2}{3} - \frac{2 5}{15}

cos (7 5^{\circ}) cos (1 5^{\circ}) - sin (7 5^{\circ}) sin (1 5^{\circ})

\frac{22}{tan ( 1 2 ^{\circ} )}

cos (arctan (- \frac{2}{3}))

sin (3 0^{\circ}) \cdot 5

3 cos (\frac{5 π}{4})