Force Vector question

This is an example from my text book, not a homework question.

A force vector, F, has components of -i + j

I know the magnitude of F is the square root of 2, I need to calculate the inclination of the vector F to the x-axis. In the book it says

theta = 180degrees - arctan(1/1)

i.e. theta = 180 degrees - 45 degrees = 135 degrees. I know that the arctan of +1 is 45 degrees.

The bit that's puzzling me is why is the parameter of the arctan 1/1. Should it not be (-1/1) ?

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mqb2766

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Original post by Skybird

This is an example from my text book, not a homework question.
A force vector, F, has components of -i + j
I know the magnitude of F is the square root of 2, I need to calculate the inclination of the vector F to the x-axis. In the book it says
theta = 180degrees - arctan(1/1)
i.e. theta = 180 degrees - 45 degrees = 135 degrees. I know that the arctan of +1 is 45 degrees.
The bit that's puzzling me is why is the parameter of the arctan 1/1. Should it not be (-1/1) ?

arctan only returns valid answers for a range -90 to 90 degrees or when the x/i component is positive. Here the ans is 135 degrees (x/i compenent is -1) so a sketch of the angle/vector should explain why its 180-arctan(1/1)? Another way of expressing it would be arctan(1/-1)+180.

arctan(-1) would give -45 and it should be clear on your sketch how it relates to the true ans.

(edited 1 month ago)

Original post by Skybird

This is an example from my text book, not a homework question.

A force vector, F, has components of -i + j

I know the magnitude of F is the square root of 2, I need to calculate the inclination of the vector F to the x-axis. In the book it says

theta = 180degrees - arctan(1/1)

i.e. theta = 180 degrees - 45 degrees = 135 degrees. I know that the arctan of +1 is 45 degrees.

The bit that's puzzling me is why is the parameter of the arctan 1/1. Should it not be (-1/1) ?

Most A level students (doing Maths) should have seen the below diagram in solving the trigonometric equation.

Students are required to show the basic angle or reference angle (denoted by α) in solving trigonometric equations.

The angle for the question lies in the 2nd quadrant, using arctan(1/1) is to find the basic angle α. In doing so, we would use 180° - α to find the obtuse angle that is the required angle.

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