For the function f(x)= -1/2cos(3t+3pi)-3 Identify the amplitude, period, phase shift and vertical Shift

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For the function f(x)= -1/2cos(3t+3pi)-3 Identify the amplitude, period, phase shift and vertical Shift

Mathematics
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think about the general function \[\cos (t)\] so what do we know about cosine? that it has an amplitude of 1, that it's period is 2pi now multiplying by -1/2 to the function makes the amplitude 1/2 but the period still 2pi now when you subtract 3 from the function cosine you shift it down vertically by 3 then the phase shift is due to the 3t + 3pi so notice you can factor a 3 out so it becomes cos3(t + pi) so the phase shift is by pi to the left and the period is changed to 2pi/3

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