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Phase difference between a sine wave and a cosine wave with an extra phase constant

The same question, asked 3 times: 2 May 2023 S1*, 13 Apr 2026 S2*, 12 May 2026 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    15
    Two simple harmonic progressive waves have displacements y1⃗=a1sin⁡(2πxλ−ωt)\vec{y_1} = a_1 \sin\left(\frac{2\pi x}{\lambda} - \omega t\right) and y2=a2cos⁡(2πxλ−ωt+ϕ)y_2 = a_2 \cos\left(\frac{2\pi x}{\lambda} - \omega t + \phi\right). What is the phase difference between two waves?

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  2. Question 2

    13 Apr 2026 S2

    122
    Two waves are represented by the equations, y1=asin⁡(ωt+kx+0.57)y_1 = a\sin(\omega t + kx + 0.57) m and y2=acos⁡(ωt+kx)y_2 = a\cos(\omega t + kx) m, where xx is in metre and tt is in second. What is the phase difference between them? (π=3.14)(\pi = 3.14)

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  3. Question 3

    12 May 2026 S1

    122
    Two simple harmonic progressive waves have displacements y1=5sin⁡(2πxλ−ωt)y_1 = 5\sin\left(\dfrac{2\pi x}{\lambda} - \omega t\right) and y2=5cos⁡(2πxλ−ωt+π6)y_2 = 5\cos\left(\dfrac{2\pi x}{\lambda} - \omega t + \dfrac{\pi}{6}\right). The phase difference between the two waves is

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