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Chapter 9: Q. 6 (page 629)

The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,胃)for each point, one with r>0and the other with r<0 Express 胃 in radians .

Short Answer

Expert verified

The polar co-ordinates are(5,0.93)and(-5,4.07)

Step by step solution

01

Step 1. Value of r

The given rectangular co-ordinate is (3,4)

We know,

r=x2+y2r=32+42=9+16=25=5

02

Step 2. Value of θ

Now, the angle 胃can be found by

胃=tan-1yx胃=tan-143=tan-1(1.33)=0.93

So the point becomes,(5,0.93)

03

Step 3. Polar co-ordinate with negative value of r

Now,

when r=-5r=-5

The ray will go in the opposite direction,

胃=tan-1yx,-蟺2<胃<蟺2胃=tan-143=tan-1(1.33)=-4.07

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Most popular questions from this chapter

Match the graph with the polar equation

胃=3蟺4

An equation whose variables are polar coordinates is called a(n) ____ ______ .

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=3cos4胃

Find zw and zw. Leave the answers in polar form.

z=1-iw=1-3i

find each quantity if v=3i-5jand w=-2i+3j

v-w
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