# Find the angle between the $x$-axis and a vector

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The $x$ component of vector $A$ is 25.0 m and the $y$ component is 40.0 m.
(a) What is the magnitude of $A$?
(b) What is the angle between the direction of $A$ and the positive direction of x?

For (b) I tried using the formula $\tan \theta = \frac{a_y}{a_x} = \frac{40}{-25} = -1.6$, thus $\arctan(-1.6)=58$ degrees which does not match the answer key: $122$ degrees.

Any help is appreciated.

asked Oct 20, 2018
edited Oct 20, 2018
Why have you used $a_x=-25$ instead of $a_x=+25$?

Your result of 58 degrees is nevertheless correct. The answer key is incorrect, as a sketch confirms : the angle should be less than 90 degees.
Answer key is correct! You have to  subtract 58 deg. from 180 deg.  because question is demanding angle from positive x axis while formula give angle from negative x axis.

## 1 Answer

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You have to subtract 58 deg. from 180 deg. because question is demanding angle from positive x axis while formula give angle from negative x axis. Moreover as sammy said in the comment vector x is pointing in positive direction so you should drop that negative from the answer.

answered Jul 24, 2019 by (110 points)