Physics · Motion In A Plane · NEET
Draw the vector A from the origin and drop a perpendicular to the x-axis. You get a right triangle where A is the hypotenuse and θ is measured from the x-axis. The side lying ALONG the x-axis is adjacent to θ, so it equals hypotenuse × cos θ = A cos θ = Ax. The side going UP (parallel to y-axis) is opposite to θ, so it equals hypotenuse × sin θ = A sin θ = Ay. So cos always goes with the axis the angle is measured FROM.
It flips only when the angle is measured from the y-axis (the vertical) instead of the x-axis. If A makes angle θ with the y-axis, then the vertical part is adjacent (A cos θ) and the horizontal part is opposite (A sin θ), giving Ax = A sin θ and Ay = A cos θ. Rule to never get confused: the component ALONG the axis you measured the angle from always uses cos; the perpendicular one uses sin.
Step 1: Note the magnitude A and the angle θ measured from the x-axis. Step 2: Ax = A cos θ. Step 3: Ay = A sin θ. Step 4: Attach signs by quadrant — right is +x, up is +y. Example: a force of 20 N at 60° above the x-axis gives Ax = 20 cos 60° = 20 × 0.5 = 10 N and Ay = 20 sin 60° = 20 × 0.866 = 17.3 N. Check: Ax² + Ay² should give back A² (100 + 300 = 400 = 20²).
Two meanings are used. Ax = A cos θ and Ay = A sin θ are the scalar components (just numbers, which can be negative). When you attach the unit vectors x-hat and y-hat, you get the vector components Ax x-hat and Ay y-hat, which point along the axes. The full vector is A = Ax x-hat + Ay y-hat. For NEET numericals you mostly compute the scalar values first, then add signs.
At θ = 0° the vector lies flat along the x-axis: Ax = A cos 0° = A and Ay = A sin 0° = 0 (no vertical part). At θ = 90° it points straight up: Ax = A cos 90° = 0 and Ay = A sin 90° = A. This is a fast sanity check — if your formula gives the wrong limit, you have swapped sin and cos.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
They are two mutually perpendicular parts (along x and y axes) that together make up the vector. For a vector A at angle θ to the x-axis: Ax = A cos θ and Ay = A sin θ, and A = Ax x-hat + Ay y-hat.
Use the Pythagoras form: A = √(Ax² + Ay²). The direction is θ = tan⁻¹(Ay / Ax). This reverse process is covered in the next concept, magnitude and direction from components.
No. Since cos θ and sin θ are never more than 1, both Ax and Ay are at most equal to A (equal only when θ is 0° or 90°). If your answer gives a component bigger than A, you made an error.
Adding vectors at odd angles is hard by drawing. Resolving each into x and y parts lets you add all the x-parts and all the y-parts separately as ordinary numbers — this is the analytical method used in projectile, force and equilibrium problems throughout Class 11 Physics.
Along +x-axis and +y-axis (right and up) the components are positive; toward −x (left) and −y (down) they are negative. The formulas A cos θ and A sin θ automatically give correct signs if θ is measured anticlockwise from the +x-axis over the full 0° to 360°.
