Question

Find the polar coordinates for the point whose rectangular coordinates are (3,4). 6. Convert y x2 to polar form.

Answer 1

Answer:

1) Thus point (3,4) is represented as (5,53$^{o}$) in polar format.

2) Polar form is $r=tan(\theta )sec(\theta)$

Step-by-step explanation:

Any point (x,y) can be represented in polar format (r,θ) as

$r=\sqrt{x^{2}+y^{2}}$

$\theta =tan^{-1}(\frac{y}{x})$

Using the above formula

The point (3,4) is represented in polar format as

$r=\sqrt{3^{2}+4^{2}}\\\\r=\sqrt{9+16}=5\\\\\theta =tan^{-1}(\frac{4}{3})=53^{o}$

Thus point (3,4) is represented as (5,53$^{o}$)

2)

The given curve is $y=x^{2}$

to convert it to polar form put

$x=rcos(\theta )\\\\y=rsin(\theta )$

Thus the curve becomes

$rsin(\theta )=r^{2}\times cos^{2}(\theta )\\\\r=\frac{sin(\theta )}{cos^{2}(\theta )}\\\\r=tan(\theta )sec(\theta)$