Question

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

Answer 1

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.