# Write the formula of the function, where x is entered in radians ?

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• Ray S
Lv 7
1 month ago

The photo was a bit fuzzy. But, I think I copied it right.

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The graph of a sinusoidal function intersects its midline at (0,2) and then has a minimum point at (1,-6). Write the formula of the function where x is entered in radians.

y = A sin(b(x - c)) + D            ← The function intersects its midline at (0,2). So, D = 2.

y = A sin(b(x - c)) + 2            ← Now, the function has a minimum point at (1,-6. ).

So, the amplitude A is 8, i.e. 2 - (-6) = 8

y = 8 sin(b(x - c)) + 2             ← Now, sine graphs from the midline to a maximum or a                                                             minimum in one fourth of a period. So, ¼P falls

between points (0,2) and (1,-6) for a distance of 1

on the horizontal ... which makes 4 the length of the

period of our function. Therefore, since the length of

a period equals 2π/b, we have 4=2π/b so that b = π/2.

y = 8 sin( (π/2)(x -c) ) + 2         ← Now, since point (0,2) is the midpoint of the period

and the period has length 4, the period begins at x =  -2

instead of the usual 0 for the parent function y = sin x.

i.e our sine function is shifted 2 to the left so that c =  -2.

y = 8 sin( (π/2)(x -(-2)) ) + 2

y = 8 sin( (π/2)(x+2) ) + 2       ← ANSWER

See the graph

https://quickmath.com/webMathematica3/quickmath/gr...