What is 4pisin(2pirst^3)4s^2t(t^3)cos(2pist^3) ?

The solution to 4pisin(2pirst^3)4s^2t(t^3)cos(2pist^3) is 16pis^2t^4cos(2pist^3)sin(2pirst^3)

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simplify 4pisin(2pirst^3)4s^2t(t^3)cos(2pist^3)

simplify

4 π sin (2 π rs t^{3}) 4 s^{2} t (t^{3}) cos (2 π s t^{3})

16 π s^{2} t^{4} cos (2 π s t^{3}) sin (2 π rs t^{3})

Solution steps

4 π sin (2 π rs t^{3}) \cdot 4 s^{2} t (t^{3}) cos (2 π s t^{3})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

4 \cdot 4 = 4^{1 + 1}

= π sin (2 π rs t^{3}) \cdot 4^{1 + 1} s^{2} t t^{3} cos (2 π s t^{3})

Add the numbers:

1 + 1 = 2

= π sin (2 π rs t^{3}) \cdot 4^{2} s^{2} t t^{3} cos (2 π s t^{3})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

t t^{3} = t^{1 + 3}

= π sin (2 π rs t^{3}) \cdot 4^{2} s^{2} t^{1 + 3} cos (2 π s t^{3})

Add the numbers:

1 + 3 = 4

= π sin (2 π rs t^{3}) \cdot 4^{2} s^{2} t^{4} cos (2 π s t^{3})

4^{2} = 16

= 16 π s^{2} t^{4} cos (2 π s t^{3}) sin (2 π rs t^{3})

s im pl i f y - (x e^{- x^{2}})

s im pl i f y 2 (5.67 \cdot 1 0^{- 8}) (266.32)^{4}

s im pl i f y x^{3} (2 x^{2})

s im pl i f y 6.94 \cdot 1 0^{- 3}

s im pl i f y - x e^{- 2 x}

What is 4pisin(2pirst^3)4s^2t(t^3)cos(2pist^3) ?
The solution to 4pisin(2pirst^3)4s^2t(t^3)cos(2pist^3) is 16pis^2t^4cos(2pist^3)sin(2pirst^3)