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