Question

How do you convert `(-4,pi/6)` to rectangular form?

Answer 1

`(x,y) => (-2sqrt3,-2)`

Explanation:

`(r,theta) => (-4,pi/6)`

`pi/6=30` degrees

This means we are working with the special triangle 30-60-90

30 degrees corresponds to `1` => OPPOSITE SIDE
60 degrees corresponds to `sqrt3` => ADJACENT SIDE
90 degrees corresponds to `2` => HYPOTENUS

cosine `=> (a d j) / (h y p)`
sine `=> (o p p) / (h y p)`

Make the necessary substitutions

`x=rcos(theta)=-4cos(pi/6)=-4(sqrt3/2)=-2sqrt3`
`y=rsin(theta)=-4sin(pi/6)=-4(1/2)=-2`

`(x,y) => (-2sqrt3,-2)`

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