Find the direction of the vector <-3, -5>

The vector

V

=

(

4

,

-

3

)

is at an angle of

−

36.67

°

to the positive

x

-axis.

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.

step-by-step explanation:

options