The point is moving in the XOY plane. Vector r, whose modulus is 1m, is directed at an angle of 30 ° to the X axis.

The point is moving in the XOY plane. Vector r, whose modulus is 1m, is directed at an angle of 30 ° to the X axis. What are the projections of the vector r on the X and Y axes?

r = 1 m.
∠α = 30 °.
rх -?
rу -?
The projection of the vector r onto the X-axis in a right-angled triangle will be the adjacent leg, and the hypotenuse will be the vector r.
cosα = rх / r.
rх = r * cosα.
rх = 1 m * cos30 ° = 0.866 m.
The projection of the vector r onto the y-axis in a right-angled triangle will be the opposite leg, and the hypotenuse is the vector r.
sinα = rу / r.
rу = r * sinα.
rу = 1 m * sin30 ° = 0.5 m.
Answer: the projection of the vector r onto the X-axis rх = 0.866 m, the projection of the vector r onto the Y-axis rу = 0.5 m.