Answer:
The vector
V
=
(
4
,
-
3
)
is at an angle of
−
36.67
°
to the positive
x
-axis.
Step-by-step explanation:
I'll presume you're looking for the angle which the vector makes with the
x
-axis.
We use our old friend
tan
for this.
tan
θ
=
y
x
⇒
θ
=
tan
−
1
(
y
x
)
⇒
θ
=
tan
−
1
(
−
3
4
)
=
tan
−
1
(
−
0.75
)
⇒
θ
=
−
0.64
⇒
θ
≈
−
36.67
°
Because
tan
−
1
can only return angles between -90° and +90° (that is, in
Q
IV
or
Q
I
), we then check which quadrant the point
(
4
,
-
3
)
is in, to confirm whether we can keep this answer or if we need to add 180°.
(
4
,
-
3
)
is in quadrant 4, and so the value given by
tan
−
1
is fine as it is.
The vector
V
=
(
4
,
-
3
)
is at an angle of
−
36.67
°
to the positive
x
-axis.