1. Polar Functions
Chris Loftus

2. Unit Circle
• Polar functions are
functions based on the
unit circle!
• They are the same equations as
Sinusoidal functions, except on a polar
grid.

3. What do they mean?
• R= the number of radians
• The number of circles that that
function goes to.
Theta= The angle measure on the unit
circle

4. Unit Circle
• r=(theta)
• Opposed to y=x in regular cartesian
functions
• In cartesian coordinates x is a function
of y and in polar r is a function of
theta.

5. Converting!
• Sometimes you will need to convert between
cartesian and polar coordinates. So here are so
equations to do so!
x= rcos(theta) r=(x^2+y^2)^1/2
y=rsin(theta) Theta=Arctan(y/x)

6. Polar Grid

7. Sin
• y=sin(Theta)

8. Sin
• You notice that the equations graph
come to a circle. The diameter of the
circle is 1 just like the unit circle.

9. Limit Example
• Lim 4sin(theta)
• x->0

10. Solution
• You can see that as the function
approaches 0, it is going towards 0
closer and closer. Thus the answer is
then 0.

11. Continuity?
• Yes the function is continuous because
it continues to go on and on for infinity
in a circle!

12. Cosine
• y=cos(Theta)

13. Cosine
• You can tell from the graph the
relationship between it and the sine
graph. It is just the flipped version and
the function goes to 1 but on the xais

14. Limit Example
• Lim 16 cos(Theta)
• x->oo (infinity)

15. Solution!
• Now you can see that the circle keeps
going around and around, so that
means that the function is undefined
because it is never going towards an
actual point.

16. Continuity?
• Yes it stays continuous!

17. Tangent
• y=tan(Theta)

18. Tangent
• The function is going towards infinity
in both directions. the function is
parabola looking but because it has two
function sit is not.

19. Limit Example
• Lim 8tan(theta)
• theta-> 9

20. Solution!
• If you plug in number numerically
trying to find out what the limit is you
would fine out that the answer is 1.267.
• y=8tan(9.0001)=1.267
• y=8tan(8.9999)=1.267

21. Continuity?
• Yes! its always continuous.