Write the formula of the function, where x is entered in radians ?
- Ray SLv 71 month ago
The photo was a bit fuzzy. But, I think I copied it right.
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
- 1 month ago
the pic is far too blurry to see what the numbers are