Question

How do you convert `(1, 5pi/6)` into rectangular coordinates?

Answer 1

`(-sqrt3/2 , 1/2 )`

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

`• x = rcostheta`

`• y = rsintheta`

here r = 1 and `theta = (5pi)/6`

hence : x`= 1xxcos((5pi)/6) = cos((5pi)/6) = -cos(pi/6)`

and `y = 1xxsin((5pi)/6) = sin((5pi)/6) = sin(pi/6)`

now the exact value of `cos(pi/6) = sqrt3/2`
and the exact value of `sin(pi/6) = 1/2`

thus x =`- cos(pi/6) = - sqrt3/2`
and y `= sin(pi/6) = 1/2`