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Find the magnitude and direction angle for each vector. Give the measure of the direction angle as an angle in [0,360]

Find the magnitude and direction angle for each vector. Give the measure of the direction-example-1

1 Answer

3 votes

Answer:

(b) 10; 150°

Explanation:

You want the polar coordinate equivalent of (-5√3, -5).

Conversion

The polar form of (a, b) is ...

(a, b) = (r; θ)

where ...

r = √(a² +b²)

θ = arctan(b/a) . . . . . with attention paid to quadrant

Application

For the given values, the polar form is ...

r = √((-5√3)² +5²) = √(75 +25) = 10

θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°

The angle is a quadrant II angle with a reference angle of 30°.

The polar form is (10; 150°).

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Additional comment

Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)

Find the magnitude and direction angle for each vector. Give the measure of the direction-example-1
User Cody Smith
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