What are the components of the vector between the origin and the polar coordinate $(14, \frac{5 π}{12})$ $(14, (5pi)/12)$ ?

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Answer 1 · 2016-01-13T17:51:13

Horizontal component $x = 3.623$ $x=3.623$ units.
vertical component $y = 13.523$ $y=13.523$ units.

To convert polar form $(r, θ)$ $(r,theta)$ into rectangular components $(x, y)$ $(x,y)$ we use the transformations :

$x = r cos θ and y = r sin θ$ $x=rcostheta and y=rsintheta$ .

So in this particular case we get

$x = 14 cos (\frac{5 π}{12}) = 3.623$ $x=14cos((5pi)/12)=3.623$

$y = 14 sin (\frac{5 π}{12}) = 13.523$ $y=14sin((5pi)/12)=13.523$

So the vector may be represented in rectangular form as $3.623 ˆ i + 13.523 ˆ j$ $3.623hati+13.523hatj$ .

What are the components of the vector between the origin and the polar coordinate (14, (5pi)/12)(14,5π12)(14, (5pi)/12)?