Plot the point (3, 2pi/3), given in polar coordinates, and find other polar coordinates (r, θ )of the point for which the following are true.

(a) r> 0, -2 pi < 0
(b) r < 0, 0 < 2 pi
(c) r > 0, 2 pi < 4 pi

(a)

(b)

(c)

Step-by-step explanation:

All polar coordinates of point (r, θ ) are

and

where, θ is in radian and n is an integer.

The given point is . So, all polar coordinates of point are

and

(a)

Substitute n=-1 in , to find the point for which .

Therefore, the required point is .

(b)

Substitute n=0 in , to find the point for which .

Therefore, the required point is .

(c)

Substitute n=1 in , to find the point for which .

Therefore, the required point is .

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

you have to put the graph on here with the question

step-by-step explanation: