Determine two properties of a trig function

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I've the following questions:

Find the period of the function $\text{f}\left(t\right)$ and determine the time where the function reach a local maximum for the first time for $t\ge0$.

The function is given as follows:

$$f\left(t\right)=a\cdot\left(b\cdot z+c\cdot x\right)\tag1$$

Where $a,b,c$ are real constants and:

$$z=\exp\left(rt\right)\cdot\left(y\cos\left(yt\right)+r\sin\left(yt\right)\right)\space\wedge\space x=\exp\left(rt\right)\cdot\sin\left(yt\right)\tag2$$

Where $r,y$ are real constants and $t\ge0$ is the time.


My work:

The period of the function is (I think) given by:

$$T=\frac{2\pi}{y}\tag3$$

And for the second question I tried:

$$f'(t)=0\tag4$$

But I do not how that leads to a solution