Converting periodic function from radians to time?

[jean28]

Homework Statement

Hey guys. So I have this homework exercise where I have to convert the following periodic function in radians into a periodic function in time.

f(θ) = (80/∏²) θ, -∏/2 ≤ θ ≤ ∏/2
(80/∏) - (80/∏²) θ, ∏/2 ≤ θ ≤ 3∏/2

Homework Equations

θ = ω₀ t
ω₀ = 2∏/T

The Attempt at a Solution

After substituting the relevant equations into the original equation and using a bit of logic regarding the periods and time intervals, I got the following function:

(160t)/(∏ * T) , -T/4 ≤ t ≤ T/4
(80T -160)/(∏ * T) t, T/4 ≤ t ≤ 3T/4


However, I don't know if this is the correct input. I would appreciate it if anyone could tell me if my calculations are correct.

Thank you all very much.

 

[Ibix]

I agree your algebra. However, your revised function isn't periodic; it's only defined on the range -T/4≤t<3T/4.

How can you modify the range to reflect the periodicity?