Chapter 9: Q. 45 (page 567)

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{3 π}{4})$

Short Answer

Expert verified

The rectangular coordinates corresponding to the polar coordinates $(- 2, \frac{3 π}{4})$ are $(\sqrt{2}, - \sqrt{2)}$

Step by step solution

Step 1. Given information

The given poplar coordinates of a point $(- 2, \frac{3 π}{4})$

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 $\frac{3 π}{4}$ for $θ$ in $x = r \cos θ$ to get the value of x.

$x = r \cos θ = - 2 . \cos (\frac{3 π}{4}) = - 2 . - \frac{\sqrt{2}}{2} = \sqrt{2}$

Step 3. Finding the value of y.

Substitute

- 2

for r and

\frac{3 π}{4}

for

θ

y = r \sin θ

to get the value of y.

y = r \sin θ = - 2 . \sin \frac{3 π}{4} = - 2 . \frac{\sqrt{2}}{2} = - \sqrt{2}

Therefore, the rectangular coordinates corresponding to the polar coordinates

(- 2, \frac{3 π}{4})

are

(\sqrt{2}, - \sqrt{2)}

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In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{3 π}{4})$

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.-2,3π4

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

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

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Study anywhere. Anytime. Across all devices.

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.
$(- 2, \frac{3 π}{4})$