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

Find the polar coordinates for the point whose rectangular

lifehitsjackson

31.12.2021

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 $^{o}$ )

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

to convert it to polar form put

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

Thus the curve becomes

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

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edulak5726

06.11.2022

Step-by-step explanation:

Given:

RUTS is a rectangle.

To prove:

∠USR ≅ ∠SUT

Statements Reasons

1. RUTS is a rectangle 1. Given

2. RU = ST, UT = RS 2. By the definition of a rectangle

3. ∠STU = ∠SRU = 90° 3. Definition of a rectangle

4. ΔURS ≅ ΔSTU 4. By the LL theorem of congruence

5. ∠USR ≅ ∠SUT 5. CPCTC

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