the question i need help answering or verifying is
"which has the greatest amplitude, a crest or a trough, or are their amplitudes the same?"
I'm thinking their amplitudes are the same meaning the highest point in a wave the crest has the same amplitude as the trough just the crest being positive and the trough being negative.
Am i right or am i taking this question too far?
You're on the right track! The amplitude of a wave refers to the maximum displacement of a point on the wave from its equilibrium position. In the case of a transverse wave, such as a water wave or a light wave, the wave oscillates up and down perpendicular to its direction of travel.
In this context, a crest is the highest point of a wave, and a trough is the lowest point. Although they have opposite orientations (crest being positive and trough being negative), their amplitudes are indeed equal in magnitude.
To understand this further, imagine a wave traveling along a rope. The amplitude would be determined by how far the rope moves up (crest) or down (trough) from its resting position. Since amplitude measures the distance from the rest position to either extreme point, it remains the same for both the crest and the trough.