How do I find the equation of this sin function? Would it be y = -1/2 sin (3/2x)-1? Im confused about how to find amplitude and stuff when the problems ARENT on the axis. Thank you!
Trigonometric functions help?
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trigonometry
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1Your answer looks good :D Don't doubt yourself! – 2017-02-09
1 Answers
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This is a function of the type $$ f(x)=a\sin(bx+c)+d $$ where $a,b,c,d\in\Bbb R$ are to be found. First of all the amplitude $a$ is $1/2$ since the wave is between $-3/2$ and $-1/2$, from which you find immediately $d$, in fact the midpoint of $[-1,1]$ is $0$ and the midpoint of $[-3/2,-1/2]$ is $-1$, thus your function is obtained from the original sine by a translation of $-1$ which is thus the value of $d$.
Then you can finally find $b,c$ imposing for example one of the following $$ f(0)=-1\\ f(\pi/3)=-3/2\\ f(2\pi/3)=-1\\ f(\pi)=-1/2 $$ and exploiting basic properties of the sine function.