Help with vectors: Write v = (5,8) in form form (|v|cos(theta) , |v|sin(theta)

[lk899]

The vector is v = (5,8).

Write V in the form (|v|cos(theta) , |v|sin(theta).

 

[Deleted member 4993]

The vector is v = (5,8).

Write V in the form (|v|cos(theta) , |v|sin(theta).

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

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[Dr.Peterson]

The vector is v = (5,8).

Write V in the form (|v|cos(theta) , |v|sin(theta).

What is |v|?

Then, how can you find theta?

Presumably you have been taught something about this; if you have no idea how to start, perhaps you can show us your book's or teacher's definitions of these.

(Neither of the numbers in the example will be nice; were you told to write them to some number of decimal places, or exact expressions for them?)

 

[HallsofIvy]

As Dr. Peterson suggested, if you know what |v| means then it should be easy to find |v| when v= (5, 8). Once you know that, you should also know that (|v|cos(theta), |v|sin(theta))= (5, 8) means that |v|cos(theta)= 5 and |v|sin(\theta)= 8. Knowing |v|, solve either of those equations for theta.

Actually, you don't need to know what |v| means! |v|cos(theta)= 5 and |v|sin(theta)= 8 are two equations in the two unknown values |v| and theta. Unlike what you may have done with systems of equations before, here the simplest first step is to square both sides of each equation and then add.