Find the value of c and state the amplitude and period of f (?)

Question

the function f is defined, for all values of x, by $f(x) = 2sin (x/3) + c$ , where c is a constant. the graph $y = f(x)$ passes through the point $( pi/2 , -3 )$

(a) find the value of c
(b) state the amplitude and period of f
(c) sketch the graph of $f(x)$ for $0<= x <= 3pi$

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Answer 1 · 2018-08-11T08:26:35

Please see the explanation below

The function is

$f(x)=2sin(x/3)+c$

The graph passes through the point $=(pi/2, -3)$

$-3=2*sin(pi/3*1/2)+c$

$-3=2sin(pi/6)+c$

$sin(pi/6)=1/2$

$c+1=-3$

$c=-4$

The value of $c=-4$

The function is

$f(x)=2sin(x/3)-4$

The amplitude is $=2$

The perod is $T=2pi/(1/3)=6pi$

See the graph below

graph{2sin(x/3)-4 [-2.54, 48.76, -12.15, 13.5]}