How to find Phase Shift in Sin and Cos Graphs?

Imagine you're watching your favorite pendulum swing back and forth, that’s kind of like a sin or cos graph! Now, sometimes the pendulum starts its swing not from the middle but from one side, that's what we call a phase shift.

A phase shift is how much a wave moves left or right compared to where it usually starts. It’s like giving your pendulum a little push from one side before letting it go. If you start at the middle, there’s no shift, but if you start on the side, that's your phase shift!

Look at the equation of the wave:

• For sin: y = sin(x - c) → phase shift is c
• For cos: y = cos(x - c) → phase shift is also c

If you see a negative sign, like in y = sin(x + 2), that means it moved left by 2 units, just like if your pendulum started swinging from the left side!

So next time you're on a swing or watching a wave, remember: phase shift is just where the motion starts! Imagine you're watching your favorite pendulum swing back and forth, that’s kind of like a sin or cos graph! Now, sometimes the pendulum starts its swing not from the middle but from one side, that's what we call a phase shift.