Home > Precalculus > Introduction to Twelve Basic Functions

What is the transformation that maps y=cosX on to y=cos1/2 X?

Answer 1

Sadie Alexander

Transformed y= #sqrt#((1+#given # y)/2).

Use #cos (x/2)=sqrt((1+cos x)/2)#.

Here for reading #cos x# as #cos (x/2)#, instead, #y to sqrt((1+y)/2)#.

For checking, use inverse mapping, after transformation

#y= cos (x/2)#. Inversely,

#x = 2 cos^(-1) y= 2 cos^(-1#(transformed y)

#=2cos^(-1)sqrt#((1+ given y)/2))

#=2cos^(-1)sqrt((1+cos x)/2)#

#=2cos^(-1)cos (x/2)=2(x/2)=x.#

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

Answer 2

Sadie Alexander

The transformation that maps ( y = \cos(X) ) onto ( y = \cos\left(\frac{1}{2}X\right) ) involves a horizontal compression by a factor of 2. This means that every point on the graph of ( y = \cos(X) ) is compressed horizontally towards the y-axis by a factor of 2 to obtain the graph of ( y = \cos\left(\frac{1}{2}X\right) ).

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.