Home > Trigonometry > Translating Sine and Cosine Functions

How do you use transformation to graph the cosine function and determine the amplitude and period of #y=cos(-4x)#?

Answer 1

Charles Autterson

Amp is 1
Period is #-pi/2#

#Acos(B(x-C)+D#

A is the amplitude period is #(2pi)/B# C is the vertical translation D is the horizontal translation

So amp in this case is 1

Period is #(2pi)/-4=-(pi)/2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Charles Autterson

To graph the cosine function (y = \cos(-4x)), you first consider the parent cosine function (y = \cos(x)). The transformation involves a horizontal compression by a factor of 1/4 (since the coefficient of x is -4). The amplitude remains unchanged at 1, and the period is affected by the compression.

The amplitude of the cosine function remains 1.

The period of the cosine function is given by (2\pi) divided by the absolute value of the coefficient of (x), which is (|-\frac{1}{4}| = \frac{1}{4}).

Therefore, the amplitude is 1 and the period is (\frac{1}{4}).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.