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Question
write an equation of the sine function with amplitude 4, period 3 degrees, and phase shift of -30 degrees.
If f(x) = Asin(Bx+C)
A = amplitude
2*pi/|B|= period
assuming B>0, -C/B is the phase shift
note - 30 degrees is -pi/6
you want amplitude 4 then A = 4
you want period 3 degrees then 2*pi/|B| = 3 => |B| = (2/3)*pi or B = 2*pi/3
you want a phase shift of -30 degrees -C/(2*pi/3) = -pi/6 => C/(2*pi/3)= pi/6 =>
C = (2*pi/3)(pi/6)=> C = pi^2/9
thus 4sin(2*pi/3 + pi^2/9) is an equation of a sine function with amplitude 4, period 3 degrees, and with a phase shift of -30 degrees.
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Sherry Wallin
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I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.
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