# Linear independence of functions

#### shashank dwivedi

Whether Cos 3x and Cos (3x + Pi/2)are linearly independent or not in the interval (-infinity, infinity)?

My attempt:

I calculated the Wronskian that comes out to be -3 (independent of x) that signifies that this function is linearly independent because the sufficient condition for the set of functions to be linearly independent is the non-vanishing of Wronskian for atleast one point in the interval.

Am I correct?

#### topsquark

Math Team
Whether Cos 3x and Cos (3x + Pi/2)are linearly independent or not in the interval (-infinity, infinity)?

My attempt:

I calculated the Wronskian that comes out to be -3 (independent of x) that signifies that this function is linearly independent because the sufficient condition for the set of functions to be linearly independent is the non-vanishing of Wronskian for atleast one point in the interval.

Am I correct?
Yes. Also $$\displaystyle cos \left ( 3x + \dfrac{\pi}{2} \right ) = sin(3x)$$ which makes this a bit easier on the calculation. (At least in my own mind.)

-Dan

1 person

#### idontknow

Since the cos and sin are two different trigonometric functions then it proves it but the general method requires Wronskian calculation .