trigonometry?
v = 10, θ = 45°
with the magnitude and direction, how can I write this in component form?
please explain the steps and do not write an answer. I have consulted my books and am struggling to completely understand.
Thanks in advance.

answers:
Como say: :
v = 10 /_45°
v = 10 ( cos 45° + i sin 45° )
v = 10/√2 + i 10/√2
v = 5√2 + i 5√2

Amy say: x = v cos(θ)
y = v sin(θ)
Draw the vector on a coordinate grid starting at (0,0). Label the end point (x,y).
Also draw lines along the xaxis and then straight up to meet the end of the vector. You have drawn a right triangle.
The length of the line along the axis is x; the height of the vertical line is y. The length of the hypotenuse is v. The angle at the origin is θ.
Cosine is defined as the length of the adjacent side of a right triangle divided by the length of the hypotenuse:
cos(θ) = x / v
Likewise, sin(θ) = y / v
For θ > 90° the triangles are positioned a little differently and we get negative values for x and/or y.

Old Science Guy say: ...
(10cos45 i , 10sin45 j)
When you get a good response,
please consider giving a best answer.
This is the only reward we get.

az_lender say: v = 10*i*cos(45) + 10*j*sin(45)
= next step would be "the answer" !
