Phase shifts for sine and cosine
Interactive practice questions
Consider the given graph of $y=\cos\left(x+\frac{\pi}{2}\right)$y=cos(x+π2).
What is the amplitude of the function?
How can the graph of $y=\cos x$y=cosx be transformed into the graph of $y=\cos\left(x+\frac{\pi}{2}\right)$y=cos(x+π2)?
By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the left.
By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the right.
By translating it horizontally $\frac{\pi}{2}$π2 units to the right.
By changing the period of the function.
By translating it horizontally $\frac{\pi}{2}$π2 units to the left.
Consider the function $f\left(x\right)=\sin x$f(x)=sinx and $g\left(x\right)=\sin\left(x-\frac{\pi}{2}\right)$g(x)=sin(x−π2).
Consider the function $f\left(x\right)=\cos x$f(x)=cosx and $g\left(x\right)=\cos\left(x-\frac{\pi}{2}\right)$g(x)=cos(x−π2).
Consider the function $y=\sin\left(x-\frac{\pi}{2}\right)$y=sin(x−π2).