Question

can anyone please explain me this given solution why we use cos thetha sin thetha can anyone please explain this solution clearly​. what id the use of sin thetha and cos thetha and how do we use??

Answer 1

See, our goal is to find the resultant of the vectors by using the magnitude of vectors and the angle (∅) between them.

Now I assume you understood the AD² = (AB + BE)² + DE² which is just Pythagorean theorem.

See, as I mentioned above, we need the answer in ∅ and magnitude of vectors (a and b)

so we'll use mathematics here.

In a right angled triangle, the trigonometric ratios are very handy. If we know ∅, we can calculate sin∅ and cos∅, which means we can calculate the ratio P/H and B/H.

This is exactly what we will do.

We don't know the value of BE, but we do know the value of BD (which is the hypotenuse, b) and we know the angle ∅

we can write cos∅ = BE/BD = BE/b

and hence BE = bcos∅

similarly I assume you can prove that DE = bsin∅

So the answer to your question is that we are using sin∅ and cos∅ to simplify our process of finding magnitude of the resultant vector. If we stick to BE and DE, we'll have to use extra maths and calculate them first and then we'll solve it for the resultant. So tidious and lengthy right? Hence we simplify the expression using the angle and the magnitude of vectors.