Select the Graph of the Polar Equation Using Symmetry, Zeros $r = \cos 3 \theta$

question 196

Multiple Choice

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
$r = \cos 3 \theta$

• A)Symmetric with respect to the polar axis \(| r | = 1\) when \(\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi\) \(r = 0\) when \(\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }\)
• B)Symmetric with respect to the polar axis \(| r | = 1\) when \(\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi\) \(r = 0\) when \(\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }\)
• C)Symmetric with respect to the polar axis \(| r | = 1\) when \(\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi\) \(r = 0\) when \(\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }\)
• D)Symmetric with respect to the polar axis \(| r | = 1\) when \(\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi\) \(r = 0\) when \(\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }\)
• E)Symmetric with respect to the polar axis \(| r | = 1\) when \(\theta = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi\) \(r = 0\) when \(\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }\)

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Definitions:

Zero Coupon Bonds

Bonds issued at a discount from their face value, which do not pay periodic interest but are redeemed at full face value at maturity.

Effective Interest Rate

The real rate of interest taking into account the effects of compounding over a given period.

Discount

A reduction from the full amount or value of a product or service, usually to entice customers or accelerate sales.

Effective Interest Method

An accounting practice for amortizing a bond discount or premium on the basis of effective interest rate, rather than the straightforward straight-line method.