differentiate: (cos(pi*t))(sin(20*pi*t))

[gtchucker09]

Hi guys,

trying to differentiate (cos(pi*t))(sin(20*pi*t))

I have used the product rule and found so far: (cos(pi*t))(20*pi*cos(20*pi*t))+(sin(20*pi*t))(-pi*sin(pi*t))

now I am stuck on simplifying the above.

I need to prove the answer is v(t)= pi(19*cos(pi*t)cos(20*pi*t)+cos(21*pi*t)

any suggestions on where to start?

 

[Deleted member 4993]

Hi guys,

trying to differentiate (cos(pi*t))(sin(20*pi*t))

I have used the product rule and found so far: (cos(pi*t))(20*pi*cos(20*pi*t))+(sin(20*pi*t))(-pi*sin(pi*t))

now I am stuck on simplifying the above.

I need to prove the answer is v(t)= pi(19*cos(pi*t)cos(20*pi*t)+cos(21*pi*t)

any suggestions on where to start?

After differentiating, use:

cos(Θ) * cos(Φ) = 1/2 * [cos(Φ + Θ) + cos(Φ - Θ)] and

sin(Θ) * sin(Φ) = -1/2 * [cos(Φ + Θ) - cos(Φ - Θ)]

continue....

 

[Steven G]

Hi guys,

trying to differentiate (cos(pi*t))(sin(20*pi*t))

I have used the product rule and found so far: (cos(pi*t))(20*pi*cos(20*pi*t))+(sin(20*pi*t))(-pi*sin(pi*t))

now I am stuck on simplifying the above.

I need to prove the answer is v(t)= pi(19*cos(pi*t)cos(20*pi*t)+cos(21*pi*t)

any suggestions on where to start?

Before you can find v(t), which I am assuming is the velocity function, you need to have the displacement function, s(t). By any chance might s(t) = (cos(pi*t))(sin(20*pi*t))???? If so, you really need to state this.

 

[JonDwyer89]

I too am having difficulty with the same problem.

the original function is (x)t=(cos(pi*t))(sin(20*pi*t))
and we have to show that after differentiating, it can be expressed as....

v(t)=pi*(19cos(pi*t)cos(20*pi*t)+cos(21*pi*t))

with the hint: you may find the trig identity useful....

cos(A+B)=cosAcosB-sinAsinB

i have got about as far as the original poster!

any help would be amazing!

 

[sinx]

Hi guys,

trying to differentiate (cos(pi*t))(sin(20*pi*t))

I have used the product rule and found so far: (cos(pi*t))(20*pi*cos(20*pi*t))+(sin(20*pi*t))(-pi*sin(pi*t))
now I am stuck on simplifying the above.
I need to prove the answer is v(t)= pi(19*cos(pi*t)cos(20*pi*t)+cos(21*pi*t)
any suggestions on where to start?

use cosAcosB=cos(A+B)+sinAsinB;
[and sinAsinB=cosAcosB-cos(A+B)]
and combine like terms.