you a viewing a read out on an oscilloscope that shows you when different voltages in a circuit maximize. If the period of the circuit is 0.04 seconds, how much time is there between when the capacitor voltage maximizes and the inductor voltage maximizes ?

there is 0.02 sec between when the capacitor voltage maximizes and the inductor voltage maximizes

Explanation:

Given that time period T = 0.04 sec

Now as the voltage across inductor maximizes, voltage across the capacitor minimizes and vice - versa;

Now, between capacitor maximizing and Inductor maximizing, there is a time of T/2

i.e t = T/2

so from our question; Time period is 0.04sec

now

t = 0.04 / 2

t = 0.02 sec  

Therefore there is 0.02 sec between when the capacitor voltage maximizes and the inductor voltage maximizes

6 cos 34, 6 sin 34 trig