If tan∝ = 4/3, why does ∝ = 53 degrees??

[Tonia]

If tan∝ = 4/3, then why/how does ∝ = 53 degrees?? Is this from dividing like this: tan divided by 4/3 or should it be 4/3 divided by tangent??

This comes from this problem: the x and y components of a displacement vector are -3.00m and +4.00m.
What angle does this vector make with the positive x axis?

theta = 180degrees - ∝ = 127 degrees

 

[mmm4444bot]

Are you familiar with the inverse trigonometric functions?

The regular functions accept an angle measurement as input, and they output the associated trigonometric ratio.

sin(∝) = 4/5

cos(∝) = 3/5

tan(∝) = 4/3

The following functions do the inverse; they accept a trigonometric ratio as input, and they output the associated angle measurement.

arcsin(4/5) = ∝

arccos(3/5) = ∝

arctan(4/3) = ∝

You'll find these inverse functions on a scientific calculator. (Make sure that the calculator is using degree mode; otherwise, you will likely need to convert from radians.) :cool: