Chapter 10: Q 1. (page 683)

If $(x, y)$ are the rectangular coordinates of a point P and $(r, θ)$ are its polar coordinate, then $x =_$ and $y =$ .

Short Answer

Expert verified

$x = r \cos (θ) y = r \sin (θ)$

Step by step solution

Step 1. Given information

Rectangular coordinate at P is $(x, y)$

Polar coordinate at P is $(r, θ)$

Step 2. Sketch the triangle using point P

Locate sides of the right-angled triangle

opposite side is $y$

adjacent side is $x$

hypotenuse side is $r$

angle is $θ$

Now, we can locate these values into the triangle

Step 3. Finding y-coordinate

Apply the sine formula

$\sin (θ) = \frac{o p p}{h y p}$

Plug opposite and hypotenuse value

role="math" localid="1646761071652" $\sin (θ) = \frac{y}{r} r \times \frac{y}{r} = r \times \sin (θ) y = r \sin (θ)$

Step 3. Finding x-coordinate

Apply the cosine formula

$\cos (θ) = \frac{a d j}{h y p}$

Plug adjacent and hypotenuse value

$\cos (θ) = \frac{x}{r} \frac{x}{r} = \cos (θ) r \times \frac{x}{r} = r \times \cos (θ) x = r \cos (θ)$

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If $(x, y)$ are the rectangular coordinates of a point P and $(r, θ)$ are its polar coordinate, then $x =_$ and $y =$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch the triangle using point P

Step 3. Finding y-coordinate

Step 3. Finding x-coordinate

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If (x,y)are the rectangular coordinates of a point P and (r,θ)are its polar coordinate, thenx=_______andy=______.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Sketch the triangle using point P

Step 3. Finding y-coordinate

Step 3. Finding x-coordinate

One App. One Place for Learning.

Most popular questions from this chapter

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If $(x, y)$ are the rectangular coordinates of a point P and $(r, θ)$ are its polar coordinate, then $x =_$ and $y =$ .