Question

As it relates to trig ratio, the opposite side (see diagram) is equal to sine x degree/hypotenuse. If we assume that the hypotenuse is the displacement, what would the opposite and adjacent sides represent in a shm sinusoid wave?

Answer 1

Sine (x^o) = Opposite over hypotenuse

[therefore, opposite side = sin(x^o) x hypotenuse]

if opposite side = 4 units and adjacent side = 3 units

then by pythagoras' theorem,

hypotenuse = 5 units and

sin(x) = 4/5

where x is the angle from adjacent side to the hypotenuse.

these relations happen to correlate to right angle triangles where the function cosine and sine together give a relation:

sin²(x) + cos²(x) = 1

An SHM sinusoidal wave has a periodically varying displacement (varying in time). This is conveniently represented using a sine or a cosine term. So thinking that there exists an opposite side or adjacent side for the displacement of the wave is unnecessary since sine function is just capturing the periodicity of the simple harmonic motion.

Though, for the sake of answering, if we take the SHM function to be:

y = Asin(x)

where y is the displacement perpendicular to x direction and A = amplitude = y_max

then, sin(x) = y/A

so, opposite side = displacement and hypotenuse = Amplitude.