Resolution of a vector is the process of splitting up a vector (force) into two perpendicular component parts. They are called rectangular components because the two component forces are mutually perpendicular.
At an angle θ with x axis, the force R acts at a point O. R can be resolved into two rectangular components along x and y axis. Two perpendicular lines CQ and CP are drawn to x and y axis. In the right angled triangle OQC,
Cos θ = OQ / OC
OQ = OC Cos θ
we know that OC = R
OQ= R Cos θ
Therefore the horizontal component of the force R is R cosƟ.
In the right angled triangle OPC,
Cos (90-Ɵ) = OP / OC
SinƟ = OP / OC ——– Cos (90-Ɵ) = SinƟ
OP = OC SinƟ
we know that OC = R
OP = R SinƟ
The vertical component of the force R is R sinƟ