I have a final exam tomorrow and the professor gave us thederivation sheet early

Question

I have a final exam tomorrow and the professor gave us thederivation sheet early that has all of the needed equations. Iunderstand them all except one involving standing waves, this iswhat's given:

ystanding (x,t) = [const.] × sin(kx +1) sin(t + 2)

I'm used to the equation: y' (x, t) = [2ym sin(kx)]× cos(t). I do not understand three things, what"[const.]" means (constant or constructive?) and why are wemultiplying 2 different sines (as opposed to sine and cosine, likethe other equation?) I also do not understand what's theamplitude in that equation (ym.) (Obviously), trig isnot my strong suit, so please provide the identity, if one isneeded, thanks!! Like I said, It's tomorrow (5/13) so the soonerthe better! I will rate lifesaver for the first response thatproperly answers my question!

Explanation / Answer

I will answer your query step by step: 1.) here const implies a constant whose value is equal to themaximum value /amplitude of the wave. 2.) Any sine wave can be equally represented in a cos wave andvis a versa the identity is sin() = cos(90-) and viseversa hence the phase shift 2  in thefirst equation includes the 90 degree phase shift 3) ym is the half the maximum aplitude that the wave reachesthe value of which depends on the generating conditions of the wavehope that helps

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