A vector has x component -7.9 and y component 10.5 What is the direction of the vector to the nearest tenth of a degree?

Question

I tried doing tantheta=10.5/-7.9, however I keep getting a negative angle less than one degree which I hope is not right. Help!

Answer 1

you are correct to say that
tanØ = 10.5/-7.9

Try to visualize where that angle is.
Isn't it in the second quadrant?
The tangent is negative in quadrant II and in quadrant IV.
So on your calculator, find the "angle in standard position" by taking
2nd
tan
(10.5/7.9)
=
to get 53.04°
so in quadrant II Ø = 180° - 53.04° = 126.96°

You calculator has been programmed to give you the closest angle to the origin, which would be -53.04, or a clockwise rotation of 53.04, putting you in the fourth quadrant.
Since for any inverse trig function there are 2 possible solutions in one period, you will have to decide what to do with that answer.

Answer 2

Forgot to mention...

if your angle given by your calculator is less than one degree for the above calcuation, I bet your calculator is set to Radians

Look for a button something like DRG, and press it until DEG appears in your display window