Cloftus Precalc Q4benchmark Polar

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  • Cloftus Precalc Q4benchmark Polar

    1. 1. Polar Functions Chris Loftus
    2. 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. 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. 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. 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. 6. Polar Grid
    7. 7. Sin • y=sin(Theta)
    8. 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. 9. Limit Example • Lim 4sin(theta) • x->0
    10. 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. 11. Continuity? • Yes the function is continuous because it continues to go on and on for infinity in a circle!
    12. 12. Cosine • y=cos(Theta)
    13. 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. 14. Limit Example • Lim 16 cos(Theta) • x->oo (infinity)
    15. 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. 16. Continuity? • Yes it stays continuous!
    17. 17. Tangent • y=tan(Theta)
    18. 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. 19. Limit Example • Lim 8tan(theta) • theta-> 9
    20. 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. 21. Continuity? • Yes! its always continuous.

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