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.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

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step-by-step explanation: