Find the amplitude and period of y = - 3cos (2x + 3) Use your calculator to graph the function and state its symmetry. Find the first positive x-intercept using your calculator's zero function.

I wish to know if there is a way to find the amplitude and period algebraically

The amplitude is |-3| = 3.

The period, T, is obtained from

(2*pi) / T = 2

T = pi

From the calculator, the first positive zero is approximately x = 0.85

Algebraically:

The cos function takes a minimum of - 1 and a maximum value of + 1.

Therefore y can be at most - 3 or + 3.

This makes the amplitude = 3.

The general expression for the sinusoidal function is

y = Acos ((2*pi) / T + b) + k

Therefore, find T from the equation

(2*pi) / T = 2 = > T = pi.