Question

Determine the amplitude and period of the function without graphing.

y = 7/3cos (-2π/3x)

Answer 1

The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the amplitude is 7/3.

The period of a cosine function is determined by the coefficient in front of the x term. In this case, the coefficient is -2π/3. The period can be determined using the formula T = 2π/|b|, where b is the coefficient. So the period is 2π/|-2π/3| = 2π/(2π/3) = 3.

Therefore, the amplitude is 7/3 and the period is 3.