find sine and cosine function from graph

Question

I've been asked to write two equation(one sine and one cosine) for the following graph

I'm understand axis of symmetry is $y=-10$, Period is$\frac{\pi}{30}$ and amplitude is $6$, are these values correct ? how will get and equation of sine and cosine from the graph.

Any help is appreciated, also any resource to learn this topic further will be helpful,

Thank you, Arif

Answer 1

Wave-form in standard form

$$ (y-k)= A \sin \dfrac{ 2 \pi (x-h)}{\lambda} = A \cos{ [\frac{\pi}{2} -\dfrac{ 2 \pi (x-h)}{\lambda}]} $$

where we get $(h,k)$ as average values of sine wave inflection point ( below where you marked $15$) with maximum positive slope using the given crest and trough of the sine-wave for $ (x-,y-)$ coordinates to determine shifts/translations of a rigid sine curve.

$$k=\frac{-4-16}{2} = -10,\, A=6, \, h= \frac{6-24}{2} = -9, \lambda=60 \,$$

Answer 2

I tried using $Bx+C=0$, our sine function starts at $-24$ and $B=\frac{\pi}{30}$ substituting $x=-24, ~B=\frac{\pi}{30}$ in $Bx+C=0$ we get $C=\frac{24\pi}{30}$

our equation become $6\sin(\frac{\pi}{30}x+\frac{24\pi}{30})-10$. Is this correct ?

Thanks, Arif