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شائع >

sin(arcsin(1/2)+arctan(-5))

الحلّ

sin (arcsin (\frac{1}{2}) + arctan (- 5))

الحلّ

\frac{26 - 5 78}{52}

+1

عشري

- 0.75114 \dots

خطوات الحلّ

sin (arcsin (\frac{1}{2}) + arctan (- 5))

arctan (- x) = - arctan (x) :

استخدم القانون التالي

arctan (- 5) = - arctan (5)

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

Rewrite using trig identities:

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

sin (arcsin (\frac{1}{2}) - arctan (5))

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

:فعّل متطابقة الطرح لزوايا

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

= sin (arcsin (\frac{1}{2})) cos (arctan (5)) - cos (arcsin (\frac{1}{2})) sin (arctan (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:

cos (arctan (5)) = \frac{26}{26}

cos (arctan (5))

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

= \frac{1 + 5 ^{2}}{1 + 5 ^{2}}

= \frac{1 + 5 ^{2}}{1 + 5 ^{2}}

بسّط

= \frac{26}{26}

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:

sin (arctan (5)) = \frac{5 26}{26}

sin (arctan (5))

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

= \frac{5 1 + 5 ^{2}}{1 + 5 ^{2}}

= \frac{5 1 + 5 ^{2}}{1 + 5 ^{2}}

بسّط

= \frac{5 26}{26}

= \frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26}

\frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26}

بسّط:

\frac{26 - 5 78}{52}

\frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26}

\frac{1}{2} \cdot \frac{26}{26} = \frac{26}{52}

\frac{1}{2} \cdot \frac{26}{26}

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

:اضرب كسور

= \frac{1 \cdot 26}{2 \cdot 26}

1 \cdot 26 = 26 :

اضرب

= \frac{26}{2 \cdot 26}

2 \cdot 26 = 52 :

اضرب الأعداد

= \frac{26}{52}

\frac{3}{2} \cdot \frac{5 26}{26} = \frac{5 78}{52}

\frac{3}{2} \cdot \frac{5 26}{26}

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

:اضرب كسور

= \frac{3 \cdot 5 26}{2 \cdot 26}

2 \cdot 26 = 52 :

اضرب الأعداد

= \frac{5 3 26}{52}

3 \cdot 526

بسّط:

578

3 \cdot 526

a b = a \cdot b

:فعْل قانون الجذور

326 = 3 \cdot 26

= 5 3 \cdot 26

3 \cdot 26 = 78 :

اضرب الأعداد

= 578

= \frac{5 78}{52}

= \frac{26}{52} - \frac{5 78}{52}

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

فعّل القانون

= \frac{26 - 5 78}{52}

= \frac{26 - 5 78}{52}

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