Answer:
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°
