Introduction to Polar Coordinates

Polar Coordinates

Homework and Revision for SBQ 2

Multiple Select

Which angle  $$\theta$$ is in the range:  $$-2\pi\ <\ \theta<\pi$$  

• $$\theta\ =\ -\pi$$  

• $$\theta\ =\ -2\pi+\frac{\pi}{8}$$  

• $$-2\pi-\frac{\pi}{8}$$  

• 0

Multiple Select

Which angle  $$\theta$$ is in the range:  $$-2\pi\ <\ \theta<2\pi$$  

• $$\theta\ =\ -\pi$$  

• $$\theta\ =\ -2\pi+\frac{\pi}{8}$$  

• $$-2\pi-\frac{\pi}{8}$$  

• 0

Coterminal Angles 

 $\theta\ \ ,\ \theta+2\pi,\ \theta-2\pi,\ \theta+2n\pi$  are coterminal angles

Add  360n  when in degrees. 

Multiple Select

Select all the angles that are coterminal with $$120^o$$  

• $$-240^o$$  

• $$-60^o$$  

• $$840^o$$  

• $$240^o$$  

 $P\left(r,\theta\right)$ 

 $\left(-r,\ \theta+\pi\right)\ and\ \left(\ -r,\theta-\pi\right)\ and\ \left(r,\theta+2\pi\right)$  are also Polar coordinates of the point P

Multiple Select

Which pair of coordinates are  not for Point C?

• $$(2,-\frac{π}{6})$$  
  

• $$(-2,\frac{5π}{6})$$  
  

• $$(2,\frac{11π}{6})$$  
  

• $$(-2,\frac{11π}{6})$$  
  

Multiple Choice

Choose the correct graph of the polar point $$\left(-2,-\frac{\pi}{4}\right)$$  .

Multiple Choice

Which point is $$\left(-5,200\pi\right)$$ ?  

• F

• E

• B

• A

Multiple Choice

"The Polar Coordinates $$\left(r,\theta\right)$$  of a point are unique "

• Always True

• Sometimes True.

• Never True.

• How can I tell when the coordinates are not given?

Multiple Select

Select the  coordinates  for the Pole.

• $$\left(0,2\pi\right)\ \$$  
  

• $$\left(0,2021\pi\right)\$$  
  

• $$\left(1,0\right)\$$  
  

• $$\left(0,0\right)$$  
  

Polar equation of a circle of radius |a|

r = a , with a different than zero.

Multiple Select

Which of these is a polar  equation for the circle ? 

• $$r=4$$
  

• $$r=8$$
  

• $$\theta=2\pi$$

• $$r\ =\ -4$$
  

Multiple Select

which one can be an equation of the line?

• Θ =- π/4

• Θ = -5π/4

• Θ = 3π/4

• Θ = 5π/4

The distance Formula

in Polar coordinates

Multiple Choice

Find the distance between A and B

• 2

• 4

• $$0.9$$

• 2.01

Substitute to get equivalent equation for the symmetry to be true.

Multiple Choice

Describe the symmetry for the equation $$r=\ -2+3\cos2\theta$$  

• Symmetry with respect to the polar axis.

• Symmetry with respect to  $$\theta=\frac{\pi}{2}$$  

• Symmetry with respect to the Pole.

• No evident symmetry.

Multiple Choice

Describe the symmetry for the equation $$r=\ 3\sin2\theta$$  

• Symmetry with respect to the polar axis.

• Symmetry with respect to  $$\theta=\frac{\pi}{2}$$  

• Symmetry with respect to the Pole.

• No evident symmetry.

Multiple Choice

Which one is a graph for : $$r=2\sin3\theta$$  

Multiple Choice

How many Petals are in the graph of $$r=3\sin\ 2\theta$$  

• None

• 1

• 2

• 3

• 4

Multiple Choice

Which of these is more likely to ba an equation for the graph ?

• $$r=2\cos4\theta$$

• $$r=2\sin4\theta$$

• $$r=4\cos2\theta$$

• $$r=2\cos8\theta$$

Multiple Choice

Which one is an equation is for a rose graph ?

• $$r=3\cos\theta$$  

• $$r=\cos3\theta$$  
  

• $$r=2$$  
  

• $$r=3\theta$$  
  

Diameter = |a|

Multiple Choice

which equation is for the graph ?

• $$r=-\frac{3}{2}\cos\theta$$

• $$r=\frac{3}{2}\cos\theta$$

• $$r=-\frac{3}{2}\sin\theta$$

• $$r=\frac{3}{2}\sin\theta$$

Multiple Choice

What is the Polar equation?

• $$r=-\sin\theta$$

• $$r=0.5\sin\theta$$

• $$r=-\cos\theta$$

• $$r=-0.5\sin\theta$$

Note the symmetry ( Polar axis for cosine , Pole for sine )

Multiple Choice

what is the equation ?

• $$r^2=4\cos2\theta$$

• $$r=4\cos^2\theta$$

• $$r^2=\sin4\theta$$

• $$r^2=4\sin2\theta$$

Multiple Choice

what is the equation?

• $$r^2=16\sin2\theta$$

• $$r^2=16\cos2\theta$$

• $$r^2=4\sin2\theta$$

• $$r^2=4\cos2\theta$$

Multiple Choice

The equation  is $$r=n\theta$$  , what is the value of n? 

• 1

• 2

• 3

• 4