Question

The angle a vector makes with the x-axis of a coordinate system must be what size in order to make one or more of its components negative?

less than 30 degrees
between 30 and 60 degrees
between 61 and 90 degrees
greater than 90 degrees

Answer 1

Greater than 90 degrees.

Reason: For a vector with angle θ, components are x = r cosθ and y = r sinθ. Both are positive only for 0° < θ < 90°. For θ > 90° (other quadrants), at least one of cosθ or sinθ is negative (90–180: x negative; 180–270: both negative; 270–360: y negative).