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sin(arcsin(1/4)+arctan(-4))

الحلّ

sin (arcsin (\frac{1}{4}) + arctan (- 4))

الحلّ

\frac{17}{68} - \frac{255}{17}

+1

العشري

- 0.87870 \dots

خطوات الحلّ

sin (arcsin (\frac{1}{4}) + arctan (- 4))

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

استخدم القانون التالي

arctan (- 4) = - arctan (4)

= sin (arcsin (\frac{1}{4}) - arctan (4))

Rewrite using trig identities:

sin (arcsin (\frac{1}{4})) cos (arctan (4)) - cos (arcsin (\frac{1}{4})) sin (arctan (4))

sin (arcsin (\frac{1}{4}) - arctan (4))

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

:فعّل متطابقة الطرح لزوايا

= sin (arcsin (\frac{1}{4})) cos (arctan (4)) - cos (arcsin (\frac{1}{4})) sin (arctan (4))

= sin (arcsin (\frac{1}{4})) cos (arctan (4)) - cos (arcsin (\frac{1}{4})) sin (arctan (4))

Rewrite using trig identities:

sin (arcsin (\frac{1}{4})) = \frac{1}{4}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{1}{4}

Rewrite using trig identities:

cos (arctan (4)) = \frac{17}{17}

cos (arctan (4))

Rewrite using trig identities:

cos (arctan (4)) = \frac{1 + 4 ^{2}}{1 + 4 ^{2}}

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

استخدم المتطابقة التالية

= \frac{1 + 4 ^{2}}{1 + 4 ^{2}}

= \frac{1 + 4 ^{2}}{1 + 4 ^{2}}

بسّط

= \frac{17}{17}

Rewrite using trig identities:

cos (arcsin (\frac{1}{4})) = \frac{15}{4}

cos (arcsin (\frac{1}{4}))

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{15}{4}

Rewrite using trig identities:

sin (arctan (4)) = \frac{4 17}{17}

sin (arctan (4))

Rewrite using trig identities:

sin (arctan (4)) = \frac{4 1 + 4 ^{2}}{1 + 4 ^{2}}

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

استخدم المتطابقة التالية

= \frac{4 1 + 4 ^{2}}{1 + 4 ^{2}}

= \frac{4 1 + 4 ^{2}}{1 + 4 ^{2}}

بسّط

= \frac{4 17}{17}

= \frac{1}{4} \cdot \frac{17}{17} - \frac{15}{4} \cdot \frac{4 17}{17}

\frac{1}{4} \cdot \frac{17}{17} - \frac{15}{4} \cdot \frac{4 17}{17}

بسّط:

\frac{17}{68} - \frac{255}{17}

\frac{1}{4} \cdot \frac{17}{17} - \frac{15}{4} \cdot \frac{4 17}{17}

\frac{1}{4} \cdot \frac{17}{17} = \frac{17}{68}

\frac{1}{4} \cdot \frac{17}{17}

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

:اضرب كسور

= \frac{1 \cdot 17}{4 \cdot 17}

1 \cdot 17 = 17 :

اضرب

= \frac{17}{4 \cdot 17}

4 \cdot 17 = 68 :

اضرب الأعداد

= \frac{17}{68}

\frac{15}{4} \cdot \frac{4 17}{17} = \frac{255}{17}

\frac{15}{4} \cdot \frac{4 17}{17}

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

:اضرب كسور

= \frac{15 \cdot 4 17}{4 \cdot 17}

4 :

إلغ العوامل المشتركة

= \frac{15 17}{17}

1517

بسّط:

255

1517

a b = a \cdot b

:فعْل قانون الجذور

1517 = 15 \cdot 17

= 15 \cdot 17

15 \cdot 17 = 255 :

اضرب الأعداد

= 255

= \frac{255}{17}

= \frac{17}{68} - \frac{255}{17}

= \frac{17}{68} - \frac{255}{17}

أمثلة شائعة

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