y = A cos(ωx + φ)

Cosine starts at its peak: $\cos(0) = 1$, while sine starts at zero. Algebraically, $\cos\theta = \sin(\theta + \pi/2)$, so cosine is just sine shifted left by a quarter-period. Amplitude, period and phase work exactly the same way as in the sine lab.

Slide amplitude $A$, angular frequency $\omega$ and phase $\phi$. Set $\phi = -\pi/2$ and you reproduce a sine wave; set $\omega = 2$ and the period halves to $\pi$. The lab shows the peak value $A$ and the period $T = 2\pi/\omega$ for quick reference.

Alternating-current voltage in your home socket follows $V(t) = V_0\cos(\omega t)$ with $\omega = 100\pi$ rad/s (50 Hz). Tides, swinging pendulums and even the orbit of Mangalyaan in time-shifted form follow cosine curves. The lab gives a visual home for those formulas.

Cosine is symmetric about the y-axis, so $\cos(-x) = \cos x$ (even), while $\sin(-x) = -\sin x$ (odd). Board examiners love testing this with definite integrals like $\int_{-a}^{a}\cos x\,dx = 2\int_0^a\cos x\,dx$. Toggle the phase slider to feel the even symmetry.