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Chapter 10: Q 1. (page 683)

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

Short Answer

Expert verified

x=rcos(胃)y=rsin(胃)

Step by step solution

01

Step 1. Given information

Rectangular coordinate at P is (x,y)

Polar coordinate at P is(r,胃)

02

Step 2. Sketch the triangle using point P

Locate sides of the right-angled triangle

opposite side isy

adjacent side isx

hypotenuse side isr

angle is胃

Now, we can locate these values into the triangle

03

Step 3. Finding y-coordinate

Apply the sine formula

sin(胃)=opphyp

Plug opposite and hypotenuse value

role="math" localid="1646761071652" sin(胃)=yrr脳yr=r脳sin(胃)y=rsin(胃)

04

Step 3. Finding x-coordinate

Apply the cosine formula

cos(胃)=adjhyp

Plug adjacent and hypotenuse value

cos(胃)=xrxr=cos(胃)r脳xr=r脳cos(胃)x=rcos(胃)

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