I'm reading through a chapter on sinusoidal alternating waveforms and I'm having some difficulty in the section on Phase Relations. The generic expression is mentioned below for a waveform that has been shifted. Following that I posted a list of expressions that show their geometric relationship. Can someone explain the list of expressions in your own context or understanding.
I do not understand these angles and/or functions. Their meaning as well as their context in phase shifting is confusing to me. I need a better foundation of understanding to have a better intuitive approach towards problem solving. I've had Calculus 1 and I'm currently taking Calculus 2. Therefore, I'm familiar with trig functions but I just can't bring it all together.
I posted this question in the electronics forum for a better engineering standpoint. However, I feel that I also need a mathematical point of view also.
A problem that is associated with this is as follows......
What is the phase relationship between the sinusoidal waveforms?
(w) is Angular Velocity
(t) is time
(i) is a instantaneous value of current
(v) is a instantaneous value of voltage
Also numbers inside parenthesis are in degrees
i = -2cos(wt-60)
v = 3sin(wt-150)
Their solution and answer is as follows. This is the part I'm not understanding at all.
i = -2cos(wt-60) = 2cos(wt-60-180) = 2cos(wt-240)
2cos(wt-240) = 2sin(wt-240+90) = 2sin(wt-150)
v and i are in phase