Question

determine the amplitude and period of each function.

1) y = 3sin (2x-pi/2)
2) y = -3sin2 (x-pi/4)
3) y = 2cos (2x+pi)
4) y = -2cos2 (x+pi/2)

Answer 1

for y = a sin (kx) or y = a cos (kx)
the amplitude is |a| and the period is 2π/k

so for the first one, y = 3 sin (2x - π/2)
amplitude is 3 , period = 2π/2 = π

do the others the same way.

Answer 2

The amplitude is the coefficient in front of the trig term. Forget whether it is + or -.

Let a be the number in front of the x.

a = 2 pi/P, so

P = 2 pi/a

For question 1), the amplitude is 3 and the period is pi