For the following pairs of sinusoidal time functions, determine which one leads/lags and by how much. (a) ?1 (?) = 4sin (6π*104?+60°) V and?2 (?) = 2cos (6π*104?-20°) V. (b) ? (?) = 10cos (400?-75°) V and? (?) = 4sin (400?+30°) A.

The question is incomplete, the complete question is given below

"For the following pairs of sinusoidal time functions, determine which one leads/lags and by how much. (a) V1 (t) = 4sin (6π*10^4t+60°) V and V (t) 2=2cos (6π*10^4t-20°) V. (b) V (t) = 10cos (400t-75°) V and I (t) = 4sin (400t+30°) A.

Answer

A. V2 (t) leads V1 (t) by 10°

B. I (t) leads V (t) by 15°

Explanation:

First we express the relationship between sine and cosine of a value.

The expression is giving below Cos (wt) = Sin (wt+90)

Hence for the equations above, we write

a. We can v (t) as

V1 (t) = 4Sin (6π*10^4+90°-30°)

V1 (t) = 4Cos (6π*10^4-30°)

Comparing to

V2 (t) = 4Cos (6π*10^4-20°)

Comparing the angle, we notice that V2 (t) leads V1 (t) by 10°

b. We can write the current wave form as

I (t) = 4sin (400t+90°-60°)

I (t) = 4Cos (400t-60°)

If we compare with V (t) = 10cos (400t-75°)

I. e 4Cos (400t-60°) = 10cos (400t-75°)

We can conclude that I (t) leads V (t) by 15°