trig identities and finding frequencies

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feline

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Nov 24, 2012
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I have been struggling with this question, I have now done as well as I can but would like some confirmation that I am on the right tracks etc. Any help would be gratefully received as this question has been causing me difficulties for a couple of weeks now.

question is:

(1.5 + sin10000t) cos500000t

I multiplied out to get:

1.5 cos 500000t + sin10000t cos500000t

then used trig identity to get:

1.5 cos 500000t + 0.5(sin510000t + sin (-490000t)

To find frequencies I have used (2 x Pi) / omega to get

(2 x pi) / (1.5 x 500000) + (2 x Pi) / (0.5 x 510000) + (2 x Pi) / (0.5 x -490000)

I then got:

(2 xPi)/750000 + (2 x pi)/255000) + (2 x pi) / -245000

giving

0.0000084 + 0.000025 + -0.0000026

which gave

0.0000074
 
feline said:
I have been struggling with this question, I have now done as well as I can but would like some confirmation that I am on the right tracks etc. Any help would be gratefully received as this question has been causing me difficulties for a couple of weeks now.

question is:

(1.5 + sin10000t) cos500000t

I multiplied out to get:

1.5 cos 500000t + sin10000t cos500000t

then used trig identity to get:

1.5 cos 500000t + 0.5(sin510000t + sin (-490000t)

To find frequencies I have used (2 x Pi) / omega to get

(2 x pi) / (1.5 x 500000) + (2 x Pi) / (0.5 x 510000) + (2 x Pi) / (0.5 x -490000)

I then got:

(2 xPi)/750000 + (2 x pi)/255000) + (2 x pi) / -245000

giving

0.0000084 + 0.000025 + -0.0000026

which gave

0.0000074
Click to expand...

You have not stated - what you needed to do - what was the original question?

Please post the original problem first - then include your work.
 
the question

Radio carrier wave: vR = cos wRt
Audio modulating wave : vA = 1.5 + sin wAt
Resulting modulated signal: vM = (1..5 + sin wAt) cos wRt

Given that wR = 500000 rad/sec and wA = 10000 rad/sec, using the trigonometric conversion of Products to Sums, determine the frequencies contained in the modulated signal.
 
feline said:
Radio carrier wave: vR = cos wRt
Audio modulating wave : vA = 1.5 + sin wAt
Resulting modulated signal: vM = (1..5 + sin wAt) cos wRt

Given that wR = 500000 rad/sec and wA = 10000 rad/sec, using the trigonometric conversion of Products to Sums, determine the frequencies contained in the modulated signal.
Click to expand...

What will be the "expected" form of moderated signal?

Is it:

VM = A * cos(Θ) + B * sin(Ω)

or

VM = A * cos(Θ + δ)

or something else?
 
still struggling.....

Thank you for this:

Clearly VM = A * cos(Θ + δ)
Solving for Θ/t in Rad/sec

although I am struglling to understand what to do

what is Θ
what is t

Im probably being really stupid but just struggling and cant get any further which is really frustrating.
 
I have now finally got
1.5 cos 500000 + 0.5 x sin 510000 x cos -490000

= -1.48 + 0.0572

= -1.4228 rad/sec

This does not look right though, any advice? please :)
 
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