Transformations of sine and cosine curves and equations
Interactive practice questions
The graph of $f\left(x\right)$f(x) and $g\left(x\right)=f\left(x-k\right)-j$g(x)=f(x−k)−j are displayed on the same set of axes in grey and black respectively.
What transformations have occurred from $f\left(x\right)$f(x) to $g\left(x\right)$g(x)? Select all that apply.
Vertical translation of $60$60 units up.
Horizontal translation of $3^\circ$3° left.
Horizontal translation of $60^\circ$60° right.
Vertical translation of $3$3 units down.
Determine the value of $j$j.
Determine the smallest positive value of $k$k.
Consider the graphs of $y=\sin x$y=sinx and $y=5\sin\left(x+\left(\left(-60\right)\right)\right)$y=5sin(x+((−60))).
Consider the graphs of $y=\cos x$y=cosx and $y=2\cos\left(x+45^\circ\right)$y=2cos(x+45°).
The graph of $y=\sin x$y=sinx has been transformed into the graph of $y=\sin\left(x+\left(\left(-45\right)\right)\right)-2$y=sin(x+((−45)))−2.