Find two other pairs of polar coc coordinates of the given polar coordinate, one with rgt 0 and one with rlt 0. Then plot the point. (4,pi /2) (a) (r,Theta )=(4,(pi )/(2))(rgt 0)

To find two other pairs of polar coordinates for the given polar coordinate $$(4, \frac{\pi}{2})$$ , we can add or subtract multiples of $$2\pi$$ to the angle $$\Theta$$ .

(a) For $$r > 0$$ :
Adding $$2\pi$$ to the angle $$\Theta$$ :
$$(r, \Theta) = (4, \frac{\pi}{2} + 2\pi) = (4, \frac{5\pi}{2})$$

(b) For $$r < 0$$ :
Subtracting $$2\pi$$ from the angle $$\Theta$$ :
$$(r, \Theta) = (4, \frac{\pi}{2} - 2\pi) = (4, -\frac{3\pi}{2})$$

Now, let's plot the point $$(4, \frac{\pi}{2})$$ on the polar coordinate system.

To plot the point $$(4, \frac{\pi}{2})$$ , we start by drawing a horizontal line at the angle $$\frac{\pi}{2}$$ (which is 90 degrees). Then, we move 4 units along this line.

The point $$(4, \frac{\pi}{2})$$ will be located 4 units above the origin on the polar coordinate system.

Similarly, we can plot the points $$(4, \frac{5\pi}{2})$$ and $$(4, -\frac{3\pi}{2})$$ by moving 4 units along the respective lines.

In summary, the two other pairs of polar coordinates for the given polar coordinate $$(4, \frac{\pi}{2})$$ are $$(4, \frac{5\pi}{2})$$ and $$(4, -\frac{3\pi}{2})$$ .