How Do You Calculate the Angle Between a Vector and the Positive X-Axis?

[imac]

Homework Statement

The x component of a certain vector is -45.0 units and the y component is +42.0 units.

a) What is the magnitude of the vector?
61.56 units <----- I got this right

b) What is the angle between the direction of the vector and the positive direction of x? Use the convention that positive angles are measured counterclockwise from the +x axis and negative angles are measured clockwise from the +x axis.

Homework Equations

N/A

The Attempt at a Solution

For part b) I put -43.02 for the angle but that was wrong. I'm guessing I have to subtract this angle from 180 which is 136.9. Is that the correct answer for b? Any help would be appreciated. Thanks.

 

[LowlyPion]

Homework Statement

The x component of a certain vector is -45.0 units and the y component is +42.0 units.

a) What is the magnitude of the vector?
61.56 units <----- I got this right

b) What is the angle between the direction of the vector and the positive direction of x? Use the convention that positive angles are measured counterclockwise from the +x axis and negative angles are measured clockwise from the +x axis.

Homework Equations

N/A

The Attempt at a Solution

For part b) I put -43.02 for the angle but that was wrong. I'm guessing I have to subtract this angle from 180 which is 136.9. Is that the correct answer for b? Any help would be appreciated. Thanks.

Use a little bit of geometry. Look at the angle that the vector forms with the positive Y-axis. Then you can add that to 90 degrees. (Which gives you your 136.9 degrees btw.)