Trigonometric method:
The more accurate method to find RC phase angles is to use the trigonometry. Then you do not have to draw the figure and use a protractor. You are only required to punch a few buttons on your calculator.
If you know values XC and R, find ratio XC/R. If you know ratio only, call it XC /R and enter it into calculator. Be sure not to make the mistake of getting ratio upside down (R /XC). This ratio will be the negative number or zero, as XC is negative or zero, and R is mostly positive. Find arctangent (arctan or tan1) of this number. This is RC phase angle.
Always remember, while solving problems of this kind, to use the capacitive reactance for XC, and not capacitance. This means that, if you are given capacitance, you should use the formula for XC and calculate the RC phase angle after that.
Problem :
The capacitive reactance in the RC circuit is -3800 O, and resistance is 7400 O. What is phase angle?
Find ratio XC/R -3800/7400. The calculator w in display something around 0.513513513. Find arctangent, or tan-1, getting the phase angle of 27.18111109° on the calculator display. Round off to 27.18 °.