laplace transform of sin(t)cos(t) vs laplace transform sin(t)*cos(t)

[@joejoe2221hzi]

The only help I could find on this question ! Legend !

[@blackpenredpen]

I am glad!!!!

[@manuelalvarez817]

This was really well explained and direct. Good job!

[@tichaonamarariromba4838]

You are great teacher in calculus field 👏👏👏

[@tc3sean]

Thank you very much! I forgot about the simple rule with the trig ID's.

[@mortezamodarres2470]

We can deduce from LT of sint*cost that in fact sint*cost=-tsint/2.

[@kebecois71]

lifesaver ! thank you (from Canada! )

[@blackpenredpen]

My pleasure!

[@Fematika]

I really like all of the responses.

[@bradleymorgan8223]

i swear, trig identities make the world go round!

[@kumkum_upreti]

Thank you 💗

[@kingkong8542]

Tnkyou so much

[@hyeonbinlim1481]

Thanks a lot!
It was really helpful to do homework! (from South Korea)

[@mukeshmeena4588]

Thank you

[@shabbinhossain8127]

so am I allowed to use the convolution? if the signs are not there? :/

[@sweswehtun3830]

Thanks a lot,sir 💖

[@Paul-qc1jt]

Better than the textbook and lecture😂

[@Oyabun-Bandoh]

what about Laplace of (sint)^6(cost)

[@BecomeMonke]

arigathanks

[@jajaja745]

im sorry but im confused. what's the difference between the two? isn't the asterisk sign also means times/multiply?

[@blackpenredpen]

No, * means the convolution when u write it like that

[@duaajassim9025]

thank you , you are the best one

[@kumarvksudhar5704]

Thank you sir

[@anaghasnair5731]

Sir...What is Laplace transform of 'sint'...????

[@littledreamling4829]

It's 1/(s^2+1) there's a Table of Laplace transforms for basic functions which you can find on google images. Hope this helps (:

[@anaghasnair5731]

@@littledreamling4829 thank u😊sir

[@sarahmohammed6236]

Thanks

[@siddiqshadab]

Can you make video on. L{(sint+cost)^2} please.

[@sugarfrosted2005]

Siddiq Shadab Multiply it out, use linearity, the double angle formula, and the pythagorean theorem.

[@sugarfrosted2005]

The inside =(1+2sint*cost) = 1+sin(2t), then you can change it to L{1}+L{sin(2t)}, the former is 1/s, the latter is in this video.

[@JeffPB]

Ah, thank you 🙏🏽

[@akashpatel291]

Hello
Are two questions same?

[@blackpenredpen]

No. The second one is the “convolution”

[@akashpatel291]

@@blackpenredpen oh ok Thank you☺️

[@serpanavajoseantonio7119]

Awesome! :)

[@cagataysunal1130]

what happens when L{sinat*cosbt} (not convolution)? a=/=b

[@carultch]

Given:
sin(a*t) cos(b*t)
Convert to reduced trig form. This can be derived through the angle sum and difference formulas.
1/2*(sin((a - b)*t) + sin((a + b)*t))
Take the Laplace transform of both terms:
L{1/2*sin((a-b)*t)} = 1/2*(a - b)/(s^2 + (a - b)^2)
L{1/2*sin((a+b)*t)} = 1/2*(a + b)/(s^2 + (a + b)^2)
Solution:
1/2*(a - b)/(s^2 + (a - b)^2) + 1/2*(a + b)/(s^2 + (a + b)^2)

[@johnpajakgumwel4746]

Solved from me

[@fabioleo7065]

spettacolo

[@nilamanipradhan3222]

Bala video

[@FalseYoutuber]

Thank you 😍

[@ahmadalaa9761]

Thank you