Question

TRIG help
Help me to convert these equations from polar to rectangular
theta=pi/3
r=5csctheta
r^2=sintheta

Answer 1

Polar coordinates are (distance from origin, angle from +x)

Rectangular are, (distance from origin X, Distance from origin Y)

What do you know about changing from one to the other?

Answer 2

Polar to rectangular equation is
x=rcostheta
y=rsintheta

Answer 3

yeah, using a right triangle you can see those here, with sin and cosine

Answer 4

(x , y) = (r*cos(theta) , r*sin(theata) )

Answer 5

okay

Answer 6

Using the Pythagorean Theorem, you can see

[r*cos(theta) ]^2 + [r*sin(theata) ]^2 = r^2

x^2 + y^2 = r^2

Answer 7

okay got it :)

Answer 8

and with the tangent of theta, you see

tan(theta) = y / x


that is really everything

Answer 9

okay s if we have r=5csctheta, how d those theorums apply?

Answer 10

r = 5*csc(a)

remember csc(a) = 1/sin(a)

\[r = 5*\frac{ 1 }{ \sin(\theta) }\]

Answer 11

multiply both sides by sin(a)

r*sin(a) = 5

that is the y coordinate (r*sin(a))

y = 5

Answer 12

So the Polar equation
\[r = 5*\csc(\theta)\]
represents a horizontal line at y=5 in rectangular coordinates

Answer 13

check it, i havent done these in awhile

Answer 14

You see they gave you a value for r, theta is not defined and is still theta, the point is

\[(r , \theta) = (5*\csc(\theta) ~,~ \theta)\]

You rearrange r=5csc(a), to r*sin(a) = 5,
remember y=r*sin(a)

y = 5

Answer 15

\[(x , y) = (x , 5)\]

horizontal line, y=5, all points (x,5)