I am asked to calculate the phase difference between the two signals below.
$$i_1 = -4\sin(377t + 55^\circ) \hspace{0.2cm}\quad \mathrm{and}\quad \hspace{0.2cm} i_2 = 5\cos(377t - 65^\circ)$$
What I did was to convert $$i_1 = -4\sin(377t + 55^\circ)$$ to $$i_1 = 4\cos(377t + 145^\circ)$$
Then find the difference by $$145 - (-65)=210$$ Then we conclude $$i_1\hspace{0.2cm} leads \hspace{0.2cm} i_2 \hspace{0.2cm}by \hspace{0.2cm}210^\circ $$ But, let's add 360 to (since the result won't change) $$i_2 = 5\cos(377t - 65^\circ)$$ We get $$i_2 = 5\cos(377t + 295^\circ)$$
Now comparing the two we get difference to be 150 degrees,which means $$i_2\hspace{0.2cm} leads \hspace{0.2cm} i_1 \hspace{0.2cm}by \hspace{0.2cm}150^\circ $$
My questions are that,
- What is the difference between these two answers? Is the latter wrong?
- How can both lead?
- How could we rewrite the second answer in terms of i1 leading i2?