Revison and HW 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