- #1

Carson

- 2

- 0

## Homework Statement

Problem- Determine if the set of all function y(t) which have period 2pi forms a vector space under operations of function addition and multiplication of a function by a constant.

What I know- So I know this involves sin, cos, sec, and csc. Also I know that a vector space must be closed under addition and multiplication by a scalar. I'm aware of how to prove polynomials are vector spaces, but not any other function.

## Homework Equations

u+v ∈ V

c*u ∈ V

## The Attempt at a Solution

[/B]

u=a1*sin(t)+a2*cos(t)+a3*sec(t)+a4*csc(t)

v=b1*sin(t)+b2*cos(t)+a3*sec(t)+a4*csc(t)