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