No calculator, leave in exact form. Determine the amplitude, period and phase shift of the function.

Question

Determine the amplitude, period, and phase shift of the function. Then graph one period of the function. Show your steps (basic graph and all transformations).

𝑓(𝑥)=3cos(𝑥−𝜋/4)

a.) Amplitude

b.) Period

c.) Phase shift

d.) Graph

Hello! I am having trouble finding a-c. d is by far the one I'm having the most difficulty with though. How do you solve this?

Answer 1

Hi Mike O.,

Use the transformation formula: y = Asin [ B( x - C) ] + D, where

|A| is the amplitude

The period is 2π/B

Phase (horizontal) shift is C

Vertical shift is D

The same applies for the Cosine Function

For the Tangent Function, the period is π/B

For your given equation f(x) = 3cos(x-π/4);

this is y = 3cos[ 1(x - π/4)] + 0, written form of transformation formula

Amplitude is |3| = 3

Period is 2π/1 = 2π

Phase shift is π/4

To graph one period (one wavelength) use the following points (x, y):

(π/4, 3), (3π/4, 0), (5π/4, -3), (7π/4, 0), (9π/4, 3).

I hope this helps, Joe.