Chapter 9: Q. 46 (page 567)

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{2 π}{3})$

Short Answer

Expert verified

The rectangular coordinates corresponding to the polar coordinates $(- 2, \frac{2 π}{3})$ are $(1, - \sqrt{3)}$

Step by step solution

Step 1. Given information

The given poplar coordinates of a point $(- 2, \frac{2 π}{3})$

Step 2. Finding the value of x

For a point P on the terminal side of $θ$ and having polar coordinates $(r, θ)$ , the corresponding rectangular coordinates are given by $x = r \cos θ$ and $y = r \sin θ$ .
Substitute $- 2$ for r and $\frac{2 π}{3}$ for $θ$ in $x = r \cos θ$ to get the value of x.

$x = r \cos θ = - 2 . \cos (\frac{2 π}{3}) = 1$

step 3. Finding the value of y.

Substitute $- 2$ for r and $\frac{2 π}{3}$ for $θ$ in $y = r \sin θ$ to get the value of $y$ .

$y = r \sin θ = - 2 . \sin (\frac{2 π}{3}) = - \sqrt{3}$

Therefore, the rectangular coordinates corresponding to the polar coordinates $(- 2, \frac{2 π}{3})$ are $(1, - \sqrt{3)}$

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In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{2 π}{3})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of x

step 3. Finding the value of y.

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In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.-2,2π3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of x

step 3. Finding the value of y.

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{2 π}{3})$