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العربية

1/(pi^2)sin(pi(1))-((1)cos(pi(1)))/pi

الحلّ

\frac{1}{π ^{2}} sin (π (1)) - \frac{( 1 ) cos ( π ( 1 ) )}{π}

\frac{1}{π}

عشري

0.31830 \dots

خطوات الحلّ

\frac{1}{π ^{2}} sin (π (1)) - \frac{( 1 ) cos ( π ( 1 ) )}{π}

= \frac{1}{π ^{2}} sin (π 1) - \frac{1 \cdot cos ( π 1 )}{π}

بسّط:

π 1 = π

π 1

π 1 = π :

اضرب

= π

\frac{1}{π ^{2}} sin (π) - \frac{1 \cdot cos ( π )}{π} = \frac{sin ( π ) - π cos ( π )}{π ^{2}}

\frac{1}{π ^{2}} sin (π) - \frac{1 \cdot cos ( π )}{π}

\frac{1}{π ^{2}} sin (π) = \frac{sin ( π )}{π ^{2}}

\frac{1}{π ^{2}} sin (π)

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

:اضرب كسور

= \frac{1 \cdot sin ( π )}{π ^{2}}

1 \cdot sin (π) = sin (π) :

اضرب

= \frac{sin ( π )}{π ^{2}}

\frac{1 \cdot cos ( π )}{π} = \frac{cos ( π )}{π}

\frac{1 \cdot cos ( π )}{π}

1 \cdot cos (π) = cos (π) :

اضرب

= \frac{cos ( π )}{π}

= \frac{sin ( π )}{π ^{2}} - \frac{cos ( π )}{π}

π^{2}, π

المضاعف المشترك الأصغر لـ:

π^{2}

π^{2}, π

Lowest Common Multiplier (LCM)

Compute an expression comprised of factors that appear either in

π^{2}

π

= π^{2}

اكتب مجددًا الكسور بحيث يكون المقام مشترك

π^{2}

اضرب كل بسط ومقام بتعبير الذي يؤدّي إلى مقام مشترك

For

\frac{cos ( π )}{π} :

multiply the denominator and numerator by

π

\frac{cos ( π )}{π} = \frac{cos ( π ) π}{ππ} = \frac{cos ( π ) π}{π ^{2}}

= \frac{sin ( π )}{π ^{2}} - \frac{cos ( π ) π}{π ^{2}}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{sin ( π ) - cos ( π ) π}{π ^{2}}

= \frac{sin ( π ) - π cos ( π )}{π ^{2}}

استخدم المتطابقة الأساسيّة التالية:

sin (π) = 0

sin (π)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

استخدم المتطابقة الأساسيّة التالية:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= \frac{0 - π ( - 1 )}{π ^{2}}

\frac{0 - π ( - 1 )}{π ^{2}}

بسّط:

\frac{1}{π}

\frac{0 - π ( - 1 )}{π ^{2}}

- (- a) = a

فعّل القانون

= \frac{0 + π 1}{π ^{2}}

0 + π 1 = π

0 + π 1

π 1 = π :

اضرب

= 0 + π

0 + π = π

= π

= \frac{π}{π ^{2}}

π :

إلغ العوامل المشتركة

= \frac{1}{π}

= \frac{1}{π}

30 cos (3 8^{\circ})

arctan (- \frac{2.68}{3.08})

sin (sin (5))

arcsin (0.9522)

e^{- s i n (0)}