I want to ask, whether is my understanding about sine and cosine in real life is correct or not.

I came across this a question(about conventional DSB AM to be specified), where we have two signals

m(t) = 2sin(2000*pi*t) + 5sin(5000*pi*t) & c(t) = 100sin(2*pi*fc*t)

...and I need to determine the conventional DSB.

So, based on my understanding about sine and cosine in real life, they're quite similar because both are periodic signals and have the same shape(for example: sin(x) and cos(x)). The only difference is the phase of sine and cosine signals, which is 90deg out of phase to each other.

Hence, I believe it is valid to change the question to

m(t) = 2cos(2000*pi*t) + 5cos(5000*pi*t) & c(t) = 100cos(2*pi*fc*t)

...and still get the correct answer.

Is my understanding correct and if it is correct, is it really applicable in industries?

Thank you in advanced!

P.S. Sorry if my English is bad and if the question is too "beginner"