PRE-CALCULUS "Polar Coordinates" Please help

[Kelly14Anne]

Please help me know what is right about the curve given thank you.

Which of the following statements is/are true about the curve r^2 = 4cos^4 θ tan^2 θ?

• There are two values of r for every value of in the domain of the curve?
• The curve has two real numbers r, which are equal in magnitude but different in sign,for every θ from θ to 2pi.
• The curve is symmetric about the pole.
• The curve is not symmetric with respect to origin.

Which os the following statements is/are correct about the symmetry of the curve r=1/2 * sin θ cos^3 θ?

• The curve is symmetric with respect to the origin.
• The curve is not symmetric with respect to the origin.
• The curve is symmetric with respect to the y-axis.
• The curve is symmetric with respect to the x-axis.

 

[Kelly14Anne]

Can you help me determine what is true? I'm struggling solving the equations..

 

[Dr.Peterson]

Can you help me determine what is true? I'm struggling solving the equations.

We'd love to help you, but you need to show your own thoughts so we can see what help you need:

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What you are doing writing pleas in unrelated threads is not helpful. Showing work would be. Have you looked at each explanation to eliminate statements that don't make sense?

 

[Steven G]

r= (1/2)(sin t)cos³ t is positive (since 1/2 is positive) whenever sin t>0 AND cos³ t > 0 OR sin t<0 AND cos³ t <0

In the given intervals is any of the above statements true?