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Transform the Polar Equation to an Equation in Rectangular Coordinates θ=π3\theta=\frac{\pi}{3}

Question 31

Multiple Choice

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.
- θ=π3\theta=\frac{\pi}{3}
 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - \theta=\frac{\pi}{3}      A)      B)         y=\sqrt{3} x  ; line through the pole making an angle of   \frac{\pi}{3}   with the polar axis  C)        y=-\frac{\sqrt{3}}{3} x  ; line through the pole making an angle of   \frac{\pi}{\pi}   with the polar axis D)       y=-\frac{\pi}{3} ;   horizontal line   \frac{\pi}{3}   units below the pole     \left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }   center at   \left(\frac{\pi}{3}, 0\right)    in rectangular coordinates


A)
 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - \theta=\frac{\pi}{3}      A)      B)         y=\sqrt{3} x  ; line through the pole making an angle of   \frac{\pi}{3}   with the polar axis  C)        y=-\frac{\sqrt{3}}{3} x  ; line through the pole making an angle of   \frac{\pi}{\pi}   with the polar axis D)       y=-\frac{\pi}{3} ;   horizontal line   \frac{\pi}{3}   units below the pole     \left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }   center at   \left(\frac{\pi}{3}, 0\right)    in rectangular coordinates

B)
 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - \theta=\frac{\pi}{3}      A)      B)         y=\sqrt{3} x  ; line through the pole making an angle of   \frac{\pi}{3}   with the polar axis  C)        y=-\frac{\sqrt{3}}{3} x  ; line through the pole making an angle of   \frac{\pi}{\pi}   with the polar axis D)       y=-\frac{\pi}{3} ;   horizontal line   \frac{\pi}{3}   units below the pole     \left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }   center at   \left(\frac{\pi}{3}, 0\right)    in rectangular coordinates


y=3x y=\sqrt{3} x ; line through the pole making an angle of π3 \frac{\pi}{3} with the polar axis

C)
 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - \theta=\frac{\pi}{3}      A)      B)         y=\sqrt{3} x  ; line through the pole making an angle of   \frac{\pi}{3}   with the polar axis  C)        y=-\frac{\sqrt{3}}{3} x  ; line through the pole making an angle of   \frac{\pi}{\pi}   with the polar axis D)       y=-\frac{\pi}{3} ;   horizontal line   \frac{\pi}{3}   units below the pole     \left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }   center at   \left(\frac{\pi}{3}, 0\right)    in rectangular coordinates


y=33x y=-\frac{\sqrt{3}}{3} x ; line through the pole making an angle of ππ \frac{\pi}{\pi} with the polar axis
D)
 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - \theta=\frac{\pi}{3}      A)      B)         y=\sqrt{3} x  ; line through the pole making an angle of   \frac{\pi}{3}   with the polar axis  C)        y=-\frac{\sqrt{3}}{3} x  ; line through the pole making an angle of   \frac{\pi}{\pi}   with the polar axis D)       y=-\frac{\pi}{3} ;   horizontal line   \frac{\pi}{3}   units below the pole     \left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }   center at   \left(\frac{\pi}{3}, 0\right)    in rectangular coordinates
y=π3; y=-\frac{\pi}{3} ; horizontal line π3 \frac{\pi}{3} units below the pole


(xπ3) 2+y2=π29; circle, radius π3\left(x-\frac{\pi}{3}\right) ^{2}+y^{2}=\frac{\pi^{2}}{9} \text {; circle, radius } \frac{\pi}{3} \text {, }
center at (π3,0) \left(\frac{\pi}{3}, 0\right) in rectangular coordinates

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