MTH301 Practice Questions Lectures 23-45

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Practice Question Mth301 23 to 45

calculus II (Virtual University of Pakistan)

StuDocu is not sponsored or endorsed by any college or university

Practice Question Mth301 23 to 45

calculus II (Virtual University of Pakistan)

Solutions of Practice Questions

Lecture No. 23 To 45

Q1. Find all possible polar co-ordinates representations of the point P whose

rectangular co-ordinates are (3 2, 3 2)

Solution

We have

x= 3 2 and y 

For polar coordinate P r 

(3 2) ( 3 2) r x y

tan tan ( 1) y x

The point P (3 2, 3 2) lies in the fourth quadrant

When

r

When r We use the formula x=rcosθ and y=rsinθ

( cos ) 8 sin cos 8 sin cos 8sin 8sin 8sec tan cos x y r r r r r r

Q4. Convert the point (2, π/3) from polar to Cartesian coordinates.

Solution

(2, we have x=rcos =2cos

y=rsin =2sin r

Therefore, the point is (1, 3 ) in Cartesian co-ordinates.