Question

Please show all work !

Find all polar coordinates of point P = (9, 75°).

Answer 1

1) (9, 75+360n)

2) (−9, 255+360n)

Explanation:

(9, 75) is same as (9, 75 + 360)

so it would be (9, 435)

It can also be expressed as (-9, 75 + 180 degrees)

so (-9,255) degrees

In general, (9,75+360 n) for n≥0 represents half of the possible ways of representing the point : (9,75)

Answer 2

Answer with explanation:

The Position of Point in two dimensional plane , P=(9,75°)

→The general rule of writing the point (r,Ф) in terms of polar coordinates is,

x=r cos Ф , y=r sin Ф

The angle between Intial side and terminal side is Acute.

Here, r=9 units

And , Ф=75°

→→Period of Cosine and Sine is 2π.

⇒⇒So,the coordinates of Point will be

x=9 *cos (2nπ+75°), And ,y=9 *sin (2nπ+75°), where n is any integer.