an angle θ. The parallelogram OACB is next constructed. Appendix- - Appendix- - - - - - Appendix Special cases: When , then R = A+B When , then R = A-B When , then R (ii) Direction Let β be the angle between the vectors A and R . Then tan sin cos CN ON Then the diagonal OC is the resultant ( R ) passing through the common tail O.
N O θ θ β C R = A+B B sin θ B cos θ Figure . Magnitude of resultant vector by parallelogram method We next find the magnitude and direction of this resultant vector. (i) Magnitude: First extend OA to the point N, so that we get ON. Then CN is drawn perpendicular to this ON, from C.
Then ONC is a right angled triangle. We can write R ON CN OA AN CN ( ) AB cos AB cos Appendix- - Appendix- - - - - - . If y = uv, where u and v are functions of x then dy dx d dx uv u dv dx v du dx ( ) . If y is a function of x, then dy dy dx dx .
d dx e e ( ) = . d dx (ln ) = . d d (sin ) cos . d d (cos ) sin .
If y is a trigonometric function of θ and θ is the function of t, then d dt d dt (sin ) cos d dt d dt (cos ) sin