Two particles A and B execute simple harmonic motion according to the equations ) y1=3sin⁡ωt and y2=4sin⁡ωt+π2+3sin⁡ωt The phase difference between them is

Representing a quantity with phase (ωt) along x-axis any quantity with a phase (ωt+ϕ) can be represented by a vector making an angle ϕ with X-axis in the anticlockwise sense and any quantity with a phase (ωt−ϕ) can be represented by a vector making an angle ϕ with X-axis in the clockwise sense.  Phase difference ϕ=tan−1⁡43 Alternatively, given y1=3sin⁡ωt.     ......(i) and  y2=4sin⁡ωt+π2+3sin⁡ωt=4cos⁡ωt+3sin⁡ωt=545cos⁡ωt+35sin⁡ωt=5[sin⁡ϕcos⁡ωt+cos⁡ϕsin⁡ωt]=5sin⁡(ωt+ϕ)      .........(ii)From (i) and (ii), the result follows.cos⁡ϕ=35;sin⁡ϕ=45 and tan⁡ϕ=43