What is the Cartesian form of (12,5π3)?

1 Answer
256
Jan 20, 2018

(6,−6√3)

Explanation:

Remember that polar coordinates are of the form (r,θ).

Also, remember that our x-values correspond with cosine and y-values with sine.

Then, remember that our sine and cosine values come from the unit circle, where r=1. So, when changing our coordinates from polar to cartesian coordinates we are taking (r,θ)→(rcos(θ),rsin(θ)).

Notice that 5π3=2π−π3. So, we can say that θ=−π3, which is in the fourth quadrant. This means that cosine is positive, and sine is negative.

Then we can essentially say that (12,5π3)→(12cos(π3),−12sin(π3))
=(12(12),−12(√32))=(6,−6√3)

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